David J. Green

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Singular

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Cohomology of group number 30 of order 128

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

General information on the group

• The group has 2 minimal generators and exponent 8.
• It is non-abelian.
• It has p-Rank 4.
• Its center has rank 2.
• It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 4.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 4 and depth 2.
• The depth coincides with the Duflot bound.
• The Poincaré series is

  (2) · (t2  −  1/2·t  +  1/2)

  (t  +  1) · (t  −  1)4 · (t2  +  1)2

• The a-invariants are -∞,-∞,-4,-4,-4. They were obtained using the filter regular HSOP of the Benson test.

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring generators

The cohomology ring has 22 minimal generators of maximal degree 6:

1. a_1_0, a nilpotent element of degree 1
2. a_1_1, a nilpotent element of degree 1
3. a_2_0, a nilpotent element of degree 2
4. b_2_1, an element of degree 2
5. b_2_2, an element of degree 2
6. b_2_3, an element of degree 2
7. a_3_2, a nilpotent element of degree 3
8. a_3_3, a nilpotent element of degree 3
9. b_3_4, an element of degree 3
10. b_3_5, an element of degree 3
11. b_3_6, an element of degree 3
12. b_3_7, an element of degree 3
13. a_4_3, a nilpotent element of degree 4
14. a_4_5, a nilpotent element of degree 4
15. b_4_10, an element of degree 4
16. b_4_11, an element of degree 4
17. c_4_12, a Duflot regular element of degree 4
18. c_4_13, a Duflot regular element of degree 4
19. b_5_17, an element of degree 5
20. b_5_18, an element of degree 5
21. b_5_19, an element of degree 5
22. a_6_7, a nilpotent element of degree 6

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Ring relations

There are 169 minimal relations of maximal degree 12:

1. a_1_0²
2. a_1_1²
3. a_1_0·a_1_1
4. a_2_0·a_1_1
5. a_2_0·a_1_0
6. b_2_1·a_1_0
7. b_2_2·a_1_1 + b_2_2·a_1_0
8. b_2_3·a_1_1 + b_2_2·a_1_1
9. b_2_3·a_1_0 + b_2_2·a_1_1
10. a_2_0²
11. b_2_3² + b_2_2² + b_2_1·b_2_2
12. a_2_0·b_2_3 + a_2_0·b_2_2 + a_1_1·a_3_2
13. a_1_0·a_3_2
14. a_1_1·a_3_3
15. a_2_0·b_2_3 + a_2_0·b_2_2 + a_1_0·a_3_3
16. a_1_1·b_3_4 + a_2_0·b_2_2
17. a_1_0·b_3_4 + a_2_0·b_2_2
18. a_1_1·b_3_5 + a_2_0·b_2_2
19. a_1_0·b_3_5 + a_2_0·b_2_2
20. a_1_1·b_3_6 + a_2_0·b_2_3 + a_2_0·b_2_1
21. a_1_0·b_3_6 + a_2_0·b_2_2
22. a_1_1·b_3_7 + a_2_0·b_2_2
23. a_1_0·b_3_7 + a_2_0·b_2_3
24. a_2_0·a_3_2
25. b_2_3·a_3_3 + b_2_2·a_3_3
26. a_2_0·a_3_3
27. b_2_2²·a_1_0 + a_2_0·b_3_4
28. b_2_3·b_3_5 + b_2_2·b_3_4 + b_2_1·b_3_5 + b_2_3·a_3_2 + b_2_1·a_3_3
29. b_2_2²·a_1_0 + a_2_0·b_3_5
30. b_2_3·b_3_6 + b_2_3·b_3_4 + b_2_2·b_3_5 + b_2_2·b_3_4 + b_2_1·b_3_5 + b_2_1·b_3_4
       + b_2_2·a_3_2 + b_2_2²·a_1_0 + b_2_1·a_3_3 + b_2_1·a_3_2
31. b_2_3·b_3_4 + b_2_2·b_3_6 + b_2_1·b_3_5 + b_2_2²·a_1_0 + b_2_1·a_3_3
32. b_2_2²·a_1_0 + b_2_1²·a_1_1 + a_2_0·b_3_6
33. b_2_3·b_3_4 + b_2_2·b_3_5 + b_2_1·b_3_7 + b_2_1·b_3_4 + b_2_2·a_3_2
34. b_2_3·b_3_7 + b_2_3·b_3_4 + b_2_2·b_3_5 + b_2_2·b_3_4 + b_2_2²·a_1_0
35. b_2_2·b_3_7 + b_2_2·b_3_5 + b_2_1·b_3_5 + b_2_3·a_3_2 + b_2_2·a_3_2 + b_2_2²·a_1_0
       + b_2_1·a_3_3
36. b_2_2²·a_1_0 + a_2_0·b_3_7
37. a_4_3·a_1_1
38. a_4_3·a_1_0
39. a_4_5·a_1_1
40. a_4_5·a_1_0
41. b_4_10·a_1_1 + b_2_3·a_3_3
42. b_4_10·a_1_0 + b_2_3·a_3_3
43. b_4_11·a_1_1 + b_2_1·a_3_3
44. b_4_11·a_1_0
45. a_3_2²
46. a_3_2·a_3_3
47. a_3_3²
48. b_3_4² + b_2_2³ + b_2_1·b_2_2² + b_2_1²·b_2_2
49. a_3_3·b_3_5 + a_3_3·b_3_4
50. b_3_5² + b_2_2³
51. b_3_4·b_3_6 + b_2_2²·b_2_3 + b_2_1²·b_2_3 + b_2_1²·b_2_2 + a_3_2·b_3_6 + a_3_2·b_3_5
       + a_2_0·b_2_2²
52. b_3_5·b_3_6 + b_3_4·b_3_5 + b_2_2²·b_2_3 + b_2_2³ + b_2_1·b_2_2·b_2_3 + b_2_1·b_2_2²
       + a_3_3·b_3_6 + a_3_3·b_3_4 + a_3_2·b_3_5 + a_3_2·b_3_4 + a_2_0·b_2_2²
53. b_3_6² + b_2_2³ + b_2_1²·b_2_2 + b_2_1³
54. b_3_4·b_3_5 + b_2_2²·b_2_3 + b_2_1·b_2_2² + a_3_2·b_3_7 + a_3_2·b_3_5 + a_3_2·b_3_4
55. a_3_3·b_3_7 + a_3_3·b_3_4
56. b_3_4·b_3_7 + b_2_2²·b_2_3 + b_2_1·b_2_2·b_2_3 + b_2_1·b_2_2² + b_2_1²·b_2_2
       + a_3_2·b_3_5 + a_2_0·b_2_2²
57. b_3_5·b_3_7 + b_3_4·b_3_5 + b_2_2²·b_2_3 + b_2_2³ + a_3_2·b_3_5 + a_2_0·b_2_2²
58. b_3_6·b_3_7 + b_2_2³ + b_2_1·b_2_2·b_2_3 + b_2_1·b_2_2² + b_2_1²·b_2_3 + a_3_2·b_3_6
       + a_3_2·b_3_5 + a_3_2·b_3_4
59. b_3_7² + b_2_2³ + b_2_1²·b_2_2
60. b_3_4·b_3_5 + b_2_2²·b_2_3 + b_2_1·b_2_2² + a_3_2·b_3_6 + a_3_2·b_3_5 + a_3_2·b_3_4
       + b_2_1·a_4_3 + a_2_0·b_2_1²
61. a_3_3·b_3_4 + a_3_2·b_3_5 + a_3_2·b_3_4 + b_2_3·a_4_3 + a_2_0·b_2_2²
62. b_3_4·b_3_5 + b_2_2²·b_2_3 + b_2_1·b_2_2² + a_3_3·b_3_4 + a_3_2·b_3_5 + b_2_2·a_4_3
       + a_2_0·b_2_2²
63. a_2_0·a_4_3
64. b_3_4·b_3_5 + b_2_2²·b_2_3 + b_2_1·b_2_2² + a_3_3·b_3_6 + a_3_3·b_3_4 + a_3_2·b_3_4
       + b_2_1·a_4_5
65. b_3_4·b_3_5 + b_2_2²·b_2_3 + b_2_1·b_2_2² + a_3_3·b_3_4 + b_2_3·a_4_5
66. a_3_3·b_3_4 + a_3_2·b_3_5 + b_2_2·a_4_5
67. a_2_0·a_4_5
68. a_3_3·b_3_4 + a_2_0·b_4_10
69. b_3_4·b_3_5 + b_2_3·b_4_11 + b_2_3·b_4_10 + b_2_2·b_4_10 + b_2_2³ + b_2_1·b_4_10
       + b_2_1·b_2_2·b_2_3 + b_2_1²·b_2_3 + a_3_3·b_3_6 + a_3_3·b_3_4 + a_3_2·b_3_6 + a_3_2·b_3_5
       + a_2_0·b_2_2²
70. b_3_4·b_3_5 + b_2_3·b_4_10 + b_2_2·b_4_11 + b_2_2·b_4_10 + b_2_2³ + b_2_1²·b_2_2
       + a_3_2·b_3_5 + a_3_2·b_3_4 + a_2_0·b_2_2²
71. a_3_3·b_3_6 + a_3_3·b_3_4 + a_2_0·b_4_11
72. a_3_3·b_3_4 + a_1_1·b_5_17
73. a_3_3·b_3_4 + a_1_0·b_5_17
74. a_3_3·b_3_4 + a_1_1·b_5_18 + a_2_0·b_2_2²
75. a_3_3·b_3_4 + a_1_0·b_5_18 + a_2_0·b_2_2²
76. a_3_3·b_3_6 + a_3_3·b_3_4 + a_1_1·b_5_19
77. a_1_0·b_5_19
78. a_4_3·a_3_2
79. a_4_3·a_3_3
80. a_4_3·b_3_4 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + b_2_1·b_2_3·a_3_2
       + a_2_0·b_2_2·b_3_4
81. a_4_3·b_3_5 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + a_2_0·b_2_2·b_3_4
82. a_4_3·b_3_6 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + b_2_1·b_2_3·a_3_2
       + b_2_1·b_2_2·a_3_2 + b_2_1²·a_3_2 + a_2_0·b_2_2·b_3_4 + a_2_0·b_2_1·b_3_6
83. a_4_3·b_3_7 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + b_2_1·b_2_3·a_3_2
       + b_2_1·b_2_2·a_3_2 + a_2_0·b_2_2·b_3_4
84. a_4_5·a_3_2
85. a_4_5·a_3_3
86. a_4_5·b_3_4 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_1·b_2_2·a_3_2
87. a_4_5·b_3_5 + b_2_2²·a_3_3 + b_2_2²·a_3_2
88. a_4_5·b_3_6 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + b_2_1·b_2_3·a_3_2 + b_2_1²·a_3_3
89. a_4_5·b_3_7 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + b_2_1·b_2_2·a_3_2
90. b_4_10·a_3_3 + b_2_2·c_4_13·a_1_0
91. b_4_11·a_3_3 + b_2_1²·a_3_3 + a_2_0·b_2_1·b_3_6 + b_2_1·c_4_13·a_1_1
       + b_2_1·c_4_12·a_1_1
92. b_4_11·b_3_4 + b_4_10·b_3_7 + b_4_10·b_3_6 + b_4_10·b_3_5 + b_4_10·b_3_4 + b_2_2²·b_3_5
       + b_2_2²·b_3_4 + b_2_1·b_2_2·b_3_5 + b_2_1²·b_3_5 + b_2_1²·b_3_4 + b_4_11·a_3_2
       + b_2_1·b_2_2·a_3_2 + a_2_0·b_2_2·b_3_4
93. b_4_11·b_3_5 + b_4_10·b_3_7 + b_4_10·b_3_4 + b_2_2²·b_3_5 + b_2_2²·b_3_4 + b_2_1²·b_3_5
       + b_4_10·a_3_2 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + b_2_1·b_2_2·a_3_2
       + a_2_0·b_2_2·b_3_4 + a_2_0·b_2_1·b_3_6 + b_2_1·c_4_13·a_1_1 + b_2_1·c_4_12·a_1_1
94. b_4_11·b_3_7 + b_4_10·b_3_6 + b_4_10·b_3_4 + b_2_2²·b_3_5 + b_2_2²·b_3_4
       + b_2_1·b_2_2·b_3_5 + b_2_1·b_2_2·b_3_4 + b_2_1²·b_3_7 + b_4_11·a_3_2 + b_2_2²·a_3_3
       + b_2_1·b_2_2·a_3_2 + b_2_1²·a_3_3 + a_2_0·b_2_2·b_3_4
95. b_4_10·b_3_6 + b_4_10·b_3_5 + b_2_1·b_5_17 + b_4_10·a_3_2 + b_2_2²·a_3_3
       + b_2_1·b_2_3·a_3_2 + b_2_1·b_2_2·a_3_2
96. b_4_10·b_3_7 + b_2_3·b_5_17 + b_4_10·a_3_2 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3
       + b_2_2²·a_3_2 + b_2_1·b_2_2·a_3_2 + a_2_0·b_2_2·b_3_4 + b_2_2·c_4_13·a_1_0
97. b_4_10·b_3_7 + b_4_10·b_3_5 + b_4_10·b_3_4 + b_2_2·b_5_17 + b_2_2·b_2_3·a_3_2
       + b_2_2²·a_3_3 + b_2_2²·a_3_2 + a_2_0·b_2_2·b_3_4 + b_2_2·c_4_13·a_1_0
98. b_2_2²·a_3_3 + a_2_0·b_5_17
99. b_4_10·b_3_7 + b_4_10·b_3_5 + b_2_1·b_5_18 + b_2_1·b_2_2·b_3_4 + b_2_1²·b_3_7
       + b_2_1²·b_3_5 + b_4_11·a_3_2 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2
       + b_2_1²·a_3_3 + b_2_1²·a_3_2 + a_2_0·b_2_1·b_3_6
100. b_4_10·b_3_7 + b_4_10·b_3_5 + b_4_10·b_3_4 + b_2_3·b_5_18 + b_2_2²·b_3_5
        + b_2_1·b_2_2·b_3_5 + b_2_1·b_2_2·b_3_4 + b_2_1²·b_3_7 + b_2_1²·b_3_4 + b_4_10·a_3_2
        + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_2 + a_2_0·b_2_2·b_3_4 + b_2_2·c_4_12·a_1_0
101. b_4_10·b_3_5 + b_2_2·b_5_18 + b_2_2²·b_3_4 + b_2_1²·b_3_5 + b_2_2²·a_3_3
        + b_2_2²·a_3_2 + b_2_1·b_2_3·a_3_2 + b_2_1·b_2_2·a_3_2 + b_2_1²·a_3_3
        + a_2_0·b_2_2·b_3_4 + b_2_2·c_4_12·a_1_0
102. b_2_2²·a_3_3 + a_2_0·b_5_18 + a_2_0·b_2_2·b_3_4
103. b_4_11·b_3_6 + b_4_10·b_3_7 + b_4_10·b_3_4 + b_2_2²·b_3_5 + b_2_2²·b_3_4 + b_2_1·b_5_19
        + b_2_1·b_2_2·b_3_5 + b_2_1·b_2_2·b_3_4 + b_2_1²·b_3_4 + b_4_11·a_3_2 + b_4_10·a_3_2
        + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2 + b_2_1·b_2_2·a_3_2 + b_2_1²·a_3_3
        + a_2_0·b_2_2·b_3_4 + b_2_1·c_4_12·a_1_1
104. b_4_10·b_3_6 + b_4_10·b_3_4 + b_2_3·b_5_19 + b_2_1·b_2_2·b_3_4 + b_2_1²·b_3_4
        + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_2 + b_2_1·b_2_2·a_3_2 + b_2_1²·a_3_3
105. b_4_10·b_3_5 + b_4_10·b_3_4 + b_2_2·b_5_19 + b_2_1·b_2_2·b_3_5 + b_2_1²·b_3_7
        + b_2_1²·b_3_4 + b_4_10·a_3_2 + b_2_2·b_2_3·a_3_2 + b_2_2²·a_3_3 + b_2_2²·a_3_2
        + b_2_1·b_2_2·a_3_2
106. b_2_1²·a_3_3 + a_2_0·b_5_19
107. a_6_7·a_1_1
108. a_6_7·a_1_0
109. a_4_3²
110. a_4_3·a_4_5
111. a_4_5²
112. b_4_11² + b_2_1·b_2_2³ + b_2_1²·b_4_11 + b_2_1³·b_2_3 + b_2_1⁴ + b_2_1·b_2_2·a_4_3
        + b_2_1²·a_4_3 + a_2_0·b_2_1³ + b_2_1·b_2_2·c_4_13 + b_2_1²·c_4_13 + b_2_1²·c_4_12
113. b_4_10² + b_2_1·b_2_2·b_4_11 + b_2_1·b_2_2³ + b_2_1²·b_2_2·b_2_3 + b_2_2²·a_4_3
        + b_2_1·b_2_2·a_4_3 + b_2_2²·c_4_13 + b_2_1·b_2_2·c_4_13 + b_2_1·b_2_2·c_4_12
114. a_4_5·b_4_11 + a_4_3·b_4_10 + b_2_2²·a_4_3 + b_2_1·b_2_2·a_4_5 + b_2_1²·a_4_5
        + a_2_0·b_2_2³ + a_2_0·b_2_1³ + a_2_0·b_2_2·c_4_13 + a_2_0·b_2_1·c_4_13
        + a_2_0·b_2_1·c_4_12
115. b_4_10·b_4_11 + b_2_2²·b_4_11 + b_2_2³·b_2_3 + b_2_2⁴ + b_2_1·b_2_2·b_4_10
        + b_2_1·b_2_2²·b_2_3 + b_2_1³·b_2_3 + a_4_5·b_4_10 + a_4_3·b_4_11 + b_2_2²·a_4_5
        + b_2_1·b_2_2·a_4_5 + b_2_1²·a_4_5 + a_2_0·b_2_2³ + a_2_0·b_2_1·b_4_11
        + a_2_0·b_2_1³ + b_2_2·b_2_3·c_4_13 + b_2_2²·c_4_13 + b_2_1·b_2_3·c_4_13
        + b_2_1·b_2_3·c_4_12 + b_2_1·b_2_2·c_4_13 + b_2_1·b_2_2·c_4_12 + a_2_0·b_2_2·c_4_13
        + a_2_0·b_2_1·c_4_13 + a_2_0·b_2_1·c_4_12
116. a_3_2·b_5_17 + a_4_5·b_4_10 + a_4_3·b_4_10 + a_2_0·b_2_2·b_4_10
117. a_3_3·b_5_17 + a_2_0·b_2_2·c_4_13
118. b_3_4·b_5_17 + b_4_10² + b_2_2²·b_4_10 + b_2_1·b_2_2²·b_2_3 + b_2_1²·b_2_2·b_2_3
        + b_2_1²·b_2_2² + b_2_1³·b_2_2 + a_4_3·b_4_10 + b_2_1²·a_4_5 + a_2_0·b_2_1·b_4_11
        + b_2_2²·c_4_13 + b_2_1·b_2_2·c_4_13 + b_2_1·b_2_2·c_4_12 + c_4_13·a_1_0·a_3_3
        + c_4_12·a_1_0·a_3_3
119. b_3_5·b_5_17 + b_2_2²·b_4_11 + b_2_2²·b_4_10 + b_2_2³·b_2_3 + b_2_2⁴ + b_2_1·b_2_2³
        + b_2_1²·b_2_2² + a_4_5·b_4_10 + b_2_2²·a_4_5 + b_2_2²·a_4_3 + b_2_1·b_2_2·a_4_5
        + a_2_0·b_2_2³ + c_4_13·a_1_0·a_3_3 + c_4_12·a_1_0·a_3_3
120. b_3_6·b_5_17 + b_2_2²·b_4_11 + b_2_2²·b_4_10 + b_2_2³·b_2_3 + b_2_2⁴
        + b_2_1·b_2_2·b_4_10 + b_2_1·b_2_2³ + b_2_1²·b_4_10 + b_2_1²·b_2_2² + a_4_3·b_4_10
        + b_2_2²·a_4_5 + b_2_2²·a_4_3 + b_2_1·b_2_2·a_4_5 + b_2_1·b_2_2·a_4_3 + b_2_1²·a_4_5
        + a_2_0·b_2_2³ + a_2_0·b_2_1·b_4_11 + c_4_13·a_1_0·a_3_3 + c_4_12·a_1_0·a_3_3
121. b_3_7·b_5_17 + b_4_10² + b_2_2²·b_4_11 + b_2_2²·b_4_10 + b_2_2³·b_2_3 + b_2_2⁴
        + b_2_1·b_2_2·b_4_10 + b_2_1·b_2_2²·b_2_3 + b_2_1·b_2_2³ + b_2_1²·b_2_2·b_2_3
        + b_2_1³·b_2_2 + a_4_5·b_4_10 + a_4_3·b_4_10 + b_2_2²·a_4_5 + b_2_1²·a_4_5
        + a_2_0·b_2_2³ + a_2_0·b_2_1·b_4_11 + b_2_2²·c_4_13 + b_2_1·b_2_2·c_4_13
        + b_2_1·b_2_2·c_4_12 + a_2_0·b_2_2·c_4_13 + c_4_13·a_1_0·a_3_3 + c_4_12·a_1_0·a_3_3
122. a_3_2·b_5_18 + a_4_5·b_4_10 + b_2_2²·a_4_5 + b_2_2²·a_4_3 + b_2_1·b_2_2·a_4_5
        + b_2_1²·a_4_5 + a_2_0·b_2_2³ + a_2_0·b_2_1·b_4_11 + a_2_0·b_2_2·c_4_13
123. a_3_3·b_5_18 + a_2_0·b_2_2·b_4_10 + a_2_0·b_2_2·c_4_13 + c_4_12·a_1_0·a_3_3
124. b_3_4·b_5_18 + b_2_2²·b_4_11 + b_2_2²·b_4_10 + b_2_2³·b_2_3 + b_2_1·b_2_2·b_4_10
        + b_2_1²·b_2_2·b_2_3 + b_2_1³·b_2_2 + a_4_5·b_4_10 + a_4_3·b_4_10 + b_2_2²·a_4_3
        + b_2_1·b_2_2·a_4_3 + a_2_0·b_2_2·b_4_10 + a_2_0·b_2_2³ + a_2_0·b_2_2·c_4_12
125. b_3_5·b_5_18 + b_2_2²·b_4_10 + b_2_2³·b_2_3 + b_2_1·b_2_2³ + b_2_1²·b_2_2²
        + b_2_2²·a_4_3 + b_2_1·b_2_2·a_4_3 + a_2_0·b_2_2·c_4_12
126. b_3_6·b_5_18 + b_4_10² + b_2_2²·b_4_10 + b_2_2³·b_2_3 + b_2_1·b_2_2·b_4_10
        + b_2_1·b_2_2²·b_2_3 + b_2_1²·b_2_2² + b_2_1³·b_2_3 + b_2_1³·b_2_2 + a_4_5·b_4_10
        + a_4_3·b_4_11 + b_2_2²·a_4_5 + b_2_2²·a_4_3 + b_2_1·b_2_2·a_4_3 + a_2_0·b_2_2·b_4_10
        + a_2_0·b_2_1·b_4_11 + a_2_0·b_2_1³ + b_2_2²·c_4_13 + b_2_1·b_2_2·c_4_13
        + b_2_1·b_2_2·c_4_12 + a_2_0·b_2_2·c_4_13 + a_2_0·b_2_2·c_4_12 + c_4_13·a_1_0·a_3_3
127. b_3_7·b_5_18 + b_2_2²·b_4_10 + b_2_2³·b_2_3 + b_2_1·b_2_2·b_4_10 + b_2_1·b_2_2²·b_2_3
        + b_2_1·b_2_2³ + b_2_1³·b_2_2 + a_4_3·b_4_10 + b_2_1·b_2_2·a_4_5 + b_2_1·b_2_2·a_4_3
        + a_2_0·b_2_2·b_4_10 + a_2_0·b_2_2·c_4_13 + a_2_0·b_2_2·c_4_12 + c_4_12·a_1_0·a_3_3
128. a_3_2·b_5_19 + a_4_3·b_4_11 + a_4_3·b_4_10 + b_2_1·b_2_2·a_4_3 + a_2_0·b_2_2·b_4_10
        + a_2_0·b_2_1·b_4_11 + a_2_0·b_2_2·c_4_13 + c_4_13·a_1_0·a_3_3
129. a_3_3·b_5_19 + a_2_0·b_2_1·b_4_11 + a_2_0·b_2_1³ + a_2_0·b_2_1·c_4_13
        + a_2_0·b_2_1·c_4_12 + c_4_13·a_1_0·a_3_3
130. b_3_4·b_5_19 + b_2_2²·b_4_11 + b_2_2³·b_2_3 + b_2_2⁴ + b_2_1·b_2_2²·b_2_3
        + b_2_1·b_2_2³ + b_2_1²·b_4_10 + b_2_1²·b_2_2·b_2_3 + b_2_1²·b_2_2²
        + b_2_1³·b_2_3 + a_4_3·b_4_11 + b_2_2²·a_4_5 + b_2_2²·a_4_3 + b_2_1·b_2_2·a_4_5
        + b_2_1²·a_4_3 + a_2_0·b_2_2·b_4_10 + a_2_0·b_2_1³
131. b_3_5·b_5_19 + b_2_2²·b_4_11 + b_2_2³·b_2_3 + b_2_2⁴ + b_2_1·b_2_2·b_4_10
        + b_2_1²·b_2_2·b_2_3 + a_4_3·b_4_10 + b_2_2²·a_4_5 + b_2_2²·a_4_3 + b_2_1²·a_4_5
        + a_2_0·b_2_1³ + a_2_0·b_2_2·c_4_13 + a_2_0·b_2_1·c_4_13 + a_2_0·b_2_1·c_4_12
132. b_3_6·b_5_19 + b_4_11² + b_4_10² + b_2_2²·b_4_11 + b_2_2³·b_2_3 + b_2_2⁴
        + b_2_1·b_2_2·b_4_10 + b_2_1·b_2_2²·b_2_3 + b_2_1·b_2_2³ + b_2_1³·b_2_2 + b_2_1⁴
        + a_4_3·b_4_11 + b_2_2²·a_4_5 + b_2_1·b_2_2·a_4_5 + a_2_0·b_2_2·b_4_10 + b_2_2²·c_4_13
        + b_2_1·b_2_2·c_4_12 + b_2_1²·c_4_13 + b_2_1²·c_4_12 + a_2_0·b_2_1·c_4_12
133. b_3_7·b_5_19 + b_4_10² + b_2_2²·b_4_11 + b_2_2³·b_2_3 + b_2_2⁴ + b_2_1·b_2_2·b_4_10
        + b_2_1·b_2_2²·b_2_3 + b_2_1²·b_4_10 + b_2_1³·b_2_3 + a_4_3·b_4_11 + a_4_3·b_4_10
        + b_2_2²·a_4_5 + b_2_1²·a_4_5 + b_2_1²·a_4_3 + a_2_0·b_2_1·b_4_11 + a_2_0·b_2_1³
        + b_2_2²·c_4_13 + b_2_1·b_2_2·c_4_13 + b_2_1·b_2_2·c_4_12 + a_2_0·b_2_2·c_4_13
        + c_4_13·a_1_0·a_3_3
134. a_4_3·b_4_11 + b_2_1·a_6_7 + b_2_1·b_2_2·a_4_5 + b_2_1·b_2_2·a_4_3 + b_2_1²·a_4_3
        + a_2_0·b_2_1·b_4_11 + a_2_0·b_2_1³ + a_2_0·b_2_1·c_4_13 + c_4_13·a_1_0·a_3_3
135. a_4_5·b_4_10 + a_4_3·b_4_10 + b_2_3·a_6_7 + a_2_0·b_2_2·b_4_10 + c_4_12·a_1_0·a_3_3
136. a_4_5·b_4_10 + b_2_2·a_6_7 + a_2_0·b_2_2·c_4_13 + c_4_13·a_1_0·a_3_3
        + c_4_12·a_1_0·a_3_3
137. a_2_0·a_6_7
138. a_4_3·b_5_17 + b_2_2·b_4_11·a_3_2 + b_2_2²·b_2_3·a_3_2 + b_2_2³·a_3_2
        + b_2_1·b_4_10·a_3_2 + b_2_1·b_2_2²·a_3_2 + b_2_1²·b_2_2·a_3_2 + a_2_0·b_2_2·b_5_17
        + a_2_0·c_4_13·b_3_4
139. a_4_5·b_5_17 + b_2_2·b_4_11·a_3_2 + b_2_2·b_4_10·a_3_2 + b_2_2²·b_2_3·a_3_2
        + b_2_2³·a_3_2 + b_2_1·b_2_2²·a_3_2 + b_2_1²·b_2_2·a_3_2 + a_2_0·c_4_13·b_3_4
140. a_4_3·b_5_18 + b_2_2·b_4_11·a_3_2 + b_2_1·b_2_2·b_2_3·a_3_2 + b_2_1·b_2_2²·a_3_2
        + b_2_1²·b_2_3·a_3_2 + a_2_0·b_2_2²·b_3_4 + a_2_0·c_4_13·b_3_4
141. b_4_11·b_5_18 + b_2_2³·b_3_5 + b_2_2³·b_3_4 + b_2_1·b_2_2·b_5_18 + b_2_1·b_2_2·b_5_17
        + b_2_1²·b_5_18 + b_2_1²·b_5_17 + b_2_1²·b_2_2·b_3_4 + b_2_1³·b_3_7 + b_2_1³·b_3_4
        + a_4_3·b_5_17 + b_2_2·b_4_11·a_3_2 + b_2_2·b_4_10·a_3_2 + b_2_2²·b_2_3·a_3_2
        + b_2_2³·a_3_2 + b_2_1·b_2_2·b_2_3·a_3_2 + b_2_1²·b_2_3·a_3_2 + b_2_1²·b_2_2·a_3_2
        + a_2_0·b_2_2²·b_3_4 + a_2_0·b_2_1²·b_3_6 + b_2_2·c_4_13·b_3_5 + b_2_2·c_4_13·b_3_4
        + b_2_1·c_4_13·b_3_7 + b_2_1·c_4_13·b_3_5 + b_2_1·c_4_13·b_3_4 + b_2_1·c_4_12·b_3_7
        + b_2_1·c_4_12·b_3_4 + b_2_3·c_4_13·a_3_2 + b_2_1·c_4_13·a_3_3 + b_2_1·c_4_13·a_3_2
        + b_2_1·c_4_12·a_3_2 + a_2_0·c_4_13·b_3_4
142. b_4_11·b_5_17 + b_4_10·b_5_17 + b_2_2²·b_5_18 + b_2_2²·b_5_17 + b_2_2³·b_3_4
        + b_2_1·b_2_2²·b_3_4 + b_2_1²·b_5_18 + b_2_1²·b_2_2·b_3_5 + b_2_1²·b_2_2·b_3_4
        + b_2_1³·b_3_7 + b_2_1³·b_3_5 + b_2_1³·b_3_4 + b_2_2·b_4_11·a_3_2
        + b_2_2²·b_2_3·a_3_2 + b_2_1·b_4_10·a_3_2 + b_2_1·b_2_2·b_2_3·a_3_2
        + b_2_1²·b_2_3·a_3_2 + a_2_0·b_2_2²·b_3_4 + b_2_2·c_4_13·b_3_5 + b_2_1·c_4_13·b_3_7
        + b_2_1·c_4_13·b_3_5 + b_2_1·c_4_12·b_3_7 + b_2_3·c_4_13·a_3_2 + b_2_2·c_4_13·a_3_3
        + b_2_1·c_4_13·a_3_3 + b_2_1·c_4_13·a_3_2 + b_2_1·c_4_12·a_3_2 + a_2_0·c_4_13·b_3_6
        + a_2_0·c_4_12·b_3_6
143. a_4_5·b_5_18 + a_4_3·b_5_17 + b_2_2·b_4_11·a_3_2 + b_2_2·b_4_10·a_3_2 + b_2_2³·a_3_2
        + b_2_1·b_4_10·a_3_2
144. b_4_11·b_5_18 + b_4_10·b_5_18 + b_4_10·b_5_17 + b_2_2²·b_5_17 + b_2_2³·b_3_5
        + b_2_2³·b_3_4 + b_2_1·b_2_2·b_5_17 + b_2_1·b_2_2²·b_3_5 + b_2_1²·b_5_18
        + b_2_1²·b_5_17 + b_2_1²·b_2_2·b_3_4 + a_4_3·b_5_17 + b_2_2·b_4_11·a_3_2
        + b_2_1·b_2_2²·a_3_2 + b_2_1²·b_2_2·a_3_2 + a_2_0·b_2_1²·b_3_6 + b_2_2·c_4_13·a_3_3
        + b_2_2·c_4_13·a_3_2 + b_2_2·c_4_12·a_3_3 + b_2_1·c_4_13·a_3_2 + b_2_1·c_4_12·a_3_2
        + a_2_0·c_4_13·b_3_4
145. b_4_11·b_5_18 + b_4_10·b_5_17 + b_2_2³·b_3_5 + b_2_2³·b_3_4 + b_2_1·b_2_2²·b_3_5
        + b_2_1·b_2_2²·b_3_4 + b_2_1²·b_5_17 + b_2_1²·b_2_2·b_3_4 + b_2_1³·b_3_7
        + b_2_1³·b_3_5 + a_4_3·b_5_19 + a_4_3·b_5_17 + b_2_2·b_4_10·a_3_2 + b_2_2²·b_2_3·a_3_2
        + b_2_2³·a_3_2 + b_2_1²·b_2_3·a_3_2 + b_2_1³·a_3_2 + b_2_2·c_4_13·b_3_5
        + b_2_1·c_4_13·b_3_5 + b_2_1·c_4_12·b_3_5 + b_2_2·c_4_13·a_3_3 + b_2_2·c_4_13·a_3_2
        + b_2_1·c_4_13·a_3_3 + b_2_1·c_4_13·a_3_2 + b_2_1·c_4_12·a_3_3 + b_2_1·c_4_12·a_3_2
        + a_2_0·c_4_13·b_3_4
146. b_4_11·b_5_19 + b_4_11·b_5_18 + b_4_10·b_5_17 + b_2_2³·b_3_5 + b_2_2³·b_3_4
        + b_2_1·b_2_2·b_5_17 + b_2_1²·b_5_19 + b_2_1²·b_2_2·b_3_5 + b_2_1²·b_2_2·b_3_4
        + b_2_1³·b_3_6 + b_2_1³·b_3_5 + a_4_3·b_5_17 + b_2_2·b_4_11·a_3_2 + b_2_2·b_4_10·a_3_2
        + b_2_1·b_4_10·a_3_2 + b_2_1²·b_2_3·a_3_2 + a_2_0·b_2_1²·b_3_6 + b_2_2·c_4_13·b_3_5
        + b_2_1·c_4_13·b_3_7 + b_2_1·c_4_13·b_3_6 + b_2_1·c_4_13·b_3_5 + b_2_1·c_4_13·b_3_4
        + b_2_1·c_4_12·b_3_6 + b_2_2·c_4_13·a_3_3 + b_2_2·c_4_13·a_3_2 + b_2_1·c_4_13·a_3_3
        + b_2_1·c_4_12·a_3_3 + a_2_0·c_4_13·b_3_6
147. b_4_11·b_5_18 + b_4_10·b_5_17 + b_2_2³·b_3_5 + b_2_2³·b_3_4 + b_2_1·b_2_2²·b_3_5
        + b_2_1·b_2_2²·b_3_4 + b_2_1²·b_5_17 + b_2_1²·b_2_2·b_3_4 + b_2_1³·b_3_7
        + b_2_1³·b_3_5 + a_4_3·b_5_17 + b_2_2·b_4_10·a_3_2 + b_2_2²·b_2_3·a_3_2 + b_2_2³·a_3_2
        + b_2_1·b_4_11·a_3_2 + b_2_1·b_4_10·a_3_2 + b_2_1²·b_2_3·a_3_2 + b_2_1²·b_2_2·a_3_2
        + b_2_1³·a_3_2 + a_2_0·b_2_1·b_5_19 + b_2_2·c_4_13·b_3_5 + b_2_1·c_4_13·b_3_5
        + b_2_1·c_4_12·b_3_5 + b_2_2·c_4_13·a_3_3 + b_2_2·c_4_13·a_3_2 + b_2_1·c_4_13·a_3_3
        + b_2_1·c_4_13·a_3_2 + b_2_1·c_4_12·a_3_3 + b_2_1·c_4_12·a_3_2 + a_2_0·c_4_13·b_3_4
148. b_4_11·b_5_18 + b_4_10·b_5_17 + b_2_2³·b_3_5 + b_2_2³·b_3_4 + b_2_1·b_2_2²·b_3_5
        + b_2_1·b_2_2²·b_3_4 + b_2_1²·b_5_17 + b_2_1²·b_2_2·b_3_4 + b_2_1³·b_3_7
        + b_2_1³·b_3_5 + a_4_5·b_5_19 + a_4_3·b_5_17 + b_2_2·b_4_11·a_3_2 + b_2_2·b_4_10·a_3_2
        + b_2_1·b_4_11·a_3_2 + b_2_1²·b_2_2·a_3_2 + b_2_1³·a_3_2 + a_2_0·b_2_1²·b_3_6
        + b_2_2·c_4_13·b_3_5 + b_2_1·c_4_13·b_3_5 + b_2_1·c_4_12·b_3_5 + b_2_2·c_4_13·a_3_3
        + b_2_2·c_4_13·a_3_2 + b_2_1·c_4_13·a_3_3 + b_2_1·c_4_13·a_3_2 + b_2_1·c_4_12·a_3_3
        + b_2_1·c_4_12·a_3_2 + a_2_0·c_4_13·b_3_6 + a_2_0·c_4_12·b_3_6 + a_2_0·c_4_12·b_3_4
149. b_4_11·b_5_18 + b_4_10·b_5_19 + b_2_2³·b_3_5 + b_2_2³·b_3_4 + b_2_1·b_2_2·b_5_17
        + b_2_1·b_2_2²·b_3_5 + b_2_1²·b_5_17 + b_2_1²·b_2_2·b_3_4 + b_2_1³·b_3_7
        + b_2_1³·b_3_5 + b_2_1³·b_3_4 + a_4_3·b_5_17 + b_2_2·b_4_10·a_3_2 + b_2_1·b_4_10·a_3_2
        + b_2_1·b_2_2·b_2_3·a_3_2 + b_2_1²·b_2_3·a_3_2 + b_2_1²·b_2_2·a_3_2
        + a_2_0·b_2_2²·b_3_4 + a_2_0·b_2_1²·b_3_6 + b_2_1·c_4_13·b_3_7 + b_2_1·c_4_12·b_3_7
        + b_2_1·c_4_12·b_3_5 + b_2_3·c_4_13·a_3_2 + b_2_2·c_4_13·a_3_2 + b_2_1·c_4_12·a_3_3
        + a_2_0·c_4_13·b_3_6 + a_2_0·c_4_13·b_3_4 + a_2_0·c_4_12·b_3_6 + a_2_0·c_4_12·b_3_4
150. a_6_7·a_3_2
151. a_6_7·a_3_3
152. a_6_7·b_3_4 + b_2_2·b_4_11·a_3_2 + b_2_2·b_4_10·a_3_2 + b_2_2²·b_2_3·a_3_2
        + b_2_2³·a_3_2 + b_2_1·b_4_10·a_3_2 + b_2_1·b_2_2²·a_3_2 + b_2_1²·b_2_2·a_3_2
153. a_6_7·b_3_5 + b_2_2·b_4_10·a_3_2
154. a_6_7·b_3_6 + b_2_2·b_4_10·a_3_2 + b_2_1·b_4_11·a_3_2 + b_2_1·b_4_10·a_3_2
        + b_2_1·b_2_2·b_2_3·a_3_2 + b_2_1·b_2_2²·a_3_2 + b_2_1²·b_2_2·a_3_2 + b_2_1³·a_3_2
        + a_2_0·c_4_13·b_3_6 + a_2_0·c_4_13·b_3_4
155. a_6_7·b_3_7 + b_2_2·b_4_10·a_3_2 + b_2_1·b_4_10·a_3_2
156. b_5_17² + b_2_1·b_2_2²·b_4_11 + b_2_1·b_2_2⁴ + b_2_1²·b_2_2·b_4_11
        + b_2_1²·b_2_2²·b_2_3 + b_2_1²·b_2_2³ + b_2_1³·b_2_2·b_2_3 + b_2_2³·a_4_3
        + b_2_1²·b_2_2·a_4_3 + b_2_2³·c_4_13 + b_2_1·b_2_2²·c_4_12 + b_2_1²·b_2_2·c_4_13
        + b_2_1²·b_2_2·c_4_12
157. b_5_18² + b_2_2⁵ + b_2_1·b_2_2²·b_4_11 + b_2_1²·b_2_2²·b_2_3 + b_2_1²·b_2_2³
        + b_2_1⁴·b_2_2 + b_2_2³·a_4_3 + b_2_1·b_2_2²·a_4_3 + b_2_2³·c_4_13
        + b_2_1·b_2_2²·c_4_13 + b_2_1·b_2_2²·c_4_12
158. b_5_19² + b_2_1²·b_2_2·b_4_11 + b_2_1³·b_4_11 + b_2_1³·b_2_2·b_2_3
        + b_2_1³·b_2_2² + b_2_1⁴·b_2_3 + b_2_1⁵ + b_2_1·b_2_2²·a_4_3 + b_2_1³·a_4_3
        + a_2_0·b_2_1⁴ + b_2_1·b_2_2²·c_4_13 + b_2_1²·b_2_2·c_4_12 + b_2_1³·c_4_13
        + b_2_1³·c_4_12
159. b_5_18·b_5_19 + b_5_17·b_5_19 + b_2_2³·b_4_11 + b_2_2⁴·b_2_3 + b_2_2⁵
        + b_2_1·b_2_2²·b_4_11 + b_2_1²·b_2_2·b_4_10 + b_2_1²·b_2_2²·b_2_3
        + b_2_1²·b_2_2³ + b_2_1³·b_4_10 + b_4_11·a_6_7 + b_2_2³·a_4_5 + b_2_2³·a_4_3
        + b_2_1·b_2_2²·a_4_3 + b_2_1²·b_2_2·a_4_5 + b_2_1²·b_2_2·a_4_3 + b_2_1³·a_4_3
        + a_2_0·b_2_2²·b_4_10 + a_2_0·b_2_1²·b_4_11 + b_2_1·b_2_2·b_2_3·c_4_13
        + b_2_1²·b_2_3·c_4_13 + b_2_1²·b_2_3·c_4_12 + a_2_0·b_4_11·c_4_13
        + a_2_0·b_2_1²·c_4_13 + a_2_0·b_2_1²·c_4_12
160. a_4_3·a_6_7
161. b_5_17·b_5_18 + b_2_2³·b_4_10 + b_2_1·b_2_2⁴ + b_2_1²·b_2_2·b_4_11
        + b_2_1²·b_2_2³ + b_2_1³·b_2_2·b_2_3 + b_2_1⁴·b_2_2 + b_2_2·b_2_3·a_6_7
        + b_2_1²·b_2_2·a_4_5 + b_2_1²·b_2_2·a_4_3 + a_2_0·b_2_2²·b_4_10
        + b_2_2²·b_2_3·c_4_13 + b_2_1·b_2_2·b_2_3·c_4_13 + b_2_1·b_2_2·b_2_3·c_4_12
        + b_2_2·a_4_5·c_4_13 + b_2_1·a_4_5·c_4_13 + b_2_1·a_4_5·c_4_12 + a_2_0·b_4_11·c_4_13
        + a_2_0·b_4_11·c_4_12 + a_2_0·b_4_10·c_4_12
162. b_5_18·b_5_19 + b_2_2³·b_4_11 + b_2_2⁴·b_2_3 + b_2_2⁵ + b_2_1·b_2_2²·b_4_10
        + b_2_1²·b_2_2·b_4_11 + b_2_1²·b_2_2²·b_2_3 + b_2_1²·b_2_2³ + b_2_1³·b_4_10
        + b_2_1³·b_2_2·b_2_3 + b_2_1³·b_2_2² + b_2_1⁴·b_2_3 + b_2_1⁴·b_2_2 + b_2_2³·a_4_5
        + b_2_2³·a_4_3 + b_2_1·b_2_2·a_6_7 + b_2_1²·a_6_7 + b_2_1²·b_2_2·a_4_3 + b_2_1³·a_4_3
        + a_2_0·b_2_2²·b_4_10 + a_2_0·b_2_1⁴ + b_2_2²·b_2_3·c_4_13 + b_2_2³·c_4_13
        + b_2_1·b_2_2·b_2_3·c_4_13 + b_2_1·b_2_2·b_2_3·c_4_12 + b_2_1·b_2_2²·c_4_12
        + b_2_1²·b_2_2·c_4_13 + b_2_1²·b_2_2·c_4_12 + b_2_2·a_4_3·c_4_13 + b_2_1·a_4_3·c_4_13
        + b_2_1·a_4_3·c_4_12 + a_2_0·b_4_10·c_4_13 + a_2_0·b_2_1²·c_4_12
163. b_5_17·b_5_19 + b_5_17·b_5_18 + b_2_2³·b_4_10 + b_2_1·b_2_2²·b_4_11
        + b_2_1·b_2_2²·b_4_10 + b_2_1·b_2_2⁴ + b_2_1²·b_2_2·b_4_10 + b_2_1²·b_2_2³
        + b_2_1³·b_2_2² + b_2_1⁴·b_2_3 + b_2_2²·a_6_7 + b_2_1²·a_6_7 + b_2_1²·b_2_2·a_4_5
        + b_2_1²·b_2_2·a_4_3 + b_2_1³·a_4_5 + b_2_1³·a_4_3 + a_2_0·b_2_2²·b_4_10
        + b_2_2³·c_4_13 + b_2_1·b_2_2·b_2_3·c_4_13 + b_2_1·b_2_2²·c_4_12
        + b_2_1²·b_2_3·c_4_13 + b_2_1²·b_2_3·c_4_12 + b_2_1²·b_2_2·c_4_13
        + b_2_1²·b_2_2·c_4_12 + b_2_2·a_4_5·c_4_13 + b_2_1·a_4_5·c_4_13 + b_2_1·a_4_5·c_4_12
        + a_2_0·b_4_11·c_4_13 + a_2_0·b_4_11·c_4_12 + a_2_0·b_4_10·c_4_12
        + a_2_0·b_2_2²·c_4_13 + a_2_0·b_2_1²·c_4_12
164. a_4_5·a_6_7
165. b_5_18·b_5_19 + b_2_2³·b_4_11 + b_2_2⁴·b_2_3 + b_2_2⁵ + b_2_1·b_2_2²·b_4_10
        + b_2_1²·b_2_2·b_4_11 + b_2_1²·b_2_2²·b_2_3 + b_2_1²·b_2_2³ + b_2_1³·b_4_10
        + b_2_1³·b_2_2·b_2_3 + b_2_1³·b_2_2² + b_2_1⁴·b_2_3 + b_2_1⁴·b_2_2 + b_4_10·a_6_7
        + b_2_2³·a_4_5 + b_2_2³·a_4_3 + b_2_1·b_2_3·a_6_7 + b_2_1·b_2_2²·a_4_5
        + b_2_1·b_2_2²·a_4_3 + b_2_1²·a_6_7 + b_2_1³·a_4_5 + b_2_1³·a_4_3
        + a_2_0·b_2_2²·b_4_10 + a_2_0·b_2_1²·b_4_11 + a_2_0·b_2_1⁴ + b_2_2²·b_2_3·c_4_13
        + b_2_2³·c_4_13 + b_2_1·b_2_2·b_2_3·c_4_13 + b_2_1·b_2_2·b_2_3·c_4_12
        + b_2_1·b_2_2²·c_4_12 + b_2_1²·b_2_2·c_4_13 + b_2_1²·b_2_2·c_4_12
        + b_2_2·a_4_5·c_4_13 + b_2_2·a_4_3·c_4_13 + b_2_1·a_4_5·c_4_13 + b_2_1·a_4_5·c_4_12
        + b_2_1·a_4_3·c_4_13 + b_2_1·a_4_3·c_4_12 + a_2_0·b_4_11·c_4_13 + a_2_0·b_4_11·c_4_12
        + a_2_0·b_2_1²·c_4_12
166. a_6_7·b_5_18 + b_2_2²·b_4_11·a_3_2 + b_2_2²·b_4_10·a_3_2 + b_2_2³·b_2_3·a_3_2
        + b_2_2⁴·a_3_2 + b_2_1·b_2_2·b_4_11·a_3_2 + b_2_1·b_2_2·b_4_10·a_3_2
        + b_2_1²·b_4_10·a_3_2 + b_2_1²·b_2_2·b_2_3·a_3_2 + b_2_1²·b_2_2²·a_3_2
        + b_2_2²·c_4_13·a_3_2 + b_2_1·b_2_2·c_4_13·a_3_2 + b_2_1·b_2_2·c_4_12·a_3_2
167. a_6_7·b_5_19 + b_2_1·b_2_2·b_4_10·a_3_2 + b_2_1·b_2_2²·b_2_3·a_3_2
        + b_2_1·b_2_2³·a_3_2 + b_2_1²·b_4_10·a_3_2 + b_2_1²·b_2_2·b_2_3·a_3_2
        + b_2_1²·b_2_2²·a_3_2 + b_2_1³·b_2_2·a_3_2 + b_2_1⁴·a_3_2
        + b_2_2·b_2_3·c_4_13·a_3_2 + b_2_2²·c_4_13·a_3_2 + b_2_1·b_2_3·c_4_13·a_3_2
        + b_2_1·b_2_3·c_4_12·a_3_2 + b_2_1·b_2_2·c_4_12·a_3_2 + b_2_1²·c_4_13·a_3_2
        + b_2_1²·c_4_12·a_3_2 + a_2_0·c_4_13·b_5_19
168. a_6_7·b_5_17 + b_2_1·b_2_2·b_4_11·a_3_2 + b_2_1·b_2_2²·b_2_3·a_3_2
        + b_2_1²·b_4_10·a_3_2 + b_2_1²·b_2_2·b_2_3·a_3_2 + b_2_1²·b_2_2²·a_3_2
        + b_2_1³·b_2_3·a_3_2 + b_2_2·b_2_3·c_4_13·a_3_2 + b_2_1·b_2_3·c_4_13·a_3_2
        + b_2_1·b_2_3·c_4_12·a_3_2
169. a_6_7²

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Data used for Benson′s test

• Benson′s completion test succeeded in degree 12.
• The completion test was perfect: It applied in the last degree in which a generator or relation was found.
• The following is a filter regular homogeneous system of parameters:
  1. c_4_12, a Duflot regular element of degree 4
  2. c_4_13, a Duflot regular element of degree 4
  3. b_2_3 + b_2_1, an element of degree 2
  4. b_3_5 + b_3_4, an element of degree 3
• The Raw Filter Degree Type of that HSOP is [-1, -1, 4, 6, 9].
• The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

About the group

Ring generators

Ring relations

Completion information

Restriction maps

Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 2

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. a_2_0 → 0, an element of degree 2
4. b_2_1 → 0, an element of degree 2
5. b_2_2 → 0, an element of degree 2
6. b_2_3 → 0, an element of degree 2
7. a_3_2 → 0, an element of degree 3
8. a_3_3 → 0, an element of degree 3
9. b_3_4 → 0, an element of degree 3
10. b_3_5 → 0, an element of degree 3
11. b_3_6 → 0, an element of degree 3
12. b_3_7 → 0, an element of degree 3
13. a_4_3 → 0, an element of degree 4
14. a_4_5 → 0, an element of degree 4
15. b_4_10 → 0, an element of degree 4
16. b_4_11 → 0, an element of degree 4
17. c_4_12 → c_1_1⁴, an element of degree 4
18. c_4_13 → c_1_0⁴, an element of degree 4
19. b_5_17 → 0, an element of degree 5
20. b_5_18 → 0, an element of degree 5
21. b_5_19 → 0, an element of degree 5
22. a_6_7 → 0, an element of degree 6

Restriction map to a maximal el. ab. subgp. of rank 4

1. a_1_0 → 0, an element of degree 1
2. a_1_1 → 0, an element of degree 1
3. a_2_0 → 0, an element of degree 2
4. b_2_1 → c_1_2², an element of degree 2
5. b_2_2 → c_1_3² + c_1_2², an element of degree 2
6. b_2_3 → c_1_3² + c_1_2·c_1_3, an element of degree 2
7. a_3_2 → 0, an element of degree 3
8. a_3_3 → 0, an element of degree 3
9. b_3_4 → c_1_3³ + c_1_2³, an element of degree 3
10. b_3_5 → c_1_3³ + c_1_2·c_1_3² + c_1_2²·c_1_3 + c_1_2³, an element of degree 3
11. b_3_6 → c_1_3³ + c_1_2·c_1_3² + c_1_2³, an element of degree 3
12. b_3_7 → c_1_3³ + c_1_2·c_1_3², an element of degree 3
13. a_4_3 → 0, an element of degree 4
14. a_4_5 → 0, an element of degree 4
15. b_4_10 → c_1_3⁴ + c_1_2·c_1_3³ + c_1_1·c_1_2·c_1_3² + c_1_1·c_1_2³ + c_1_1²·c_1_2·c_1_3
       + c_1_1²·c_1_2² + c_1_0²·c_1_3² + c_1_0²·c_1_2·c_1_3, an element of degree 4
16. b_4_11 → c_1_2³·c_1_3 + c_1_2⁴ + c_1_1·c_1_2²·c_1_3 + c_1_1·c_1_2³ + c_1_1²·c_1_2²
       + c_1_0²·c_1_2·c_1_3, an element of degree 4
17. c_4_12 → c_1_3⁴ + c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3 + c_1_1·c_1_2³ + c_1_1²·c_1_3²
       + c_1_1⁴ + c_1_0²·c_1_3² + c_1_0²·c_1_2·c_1_3, an element of degree 4
18. c_4_13 → c_1_3⁴ + c_1_2³·c_1_3 + c_1_2⁴ + c_1_0²·c_1_2² + c_1_0⁴, an element of degree 4
19. b_5_17 → c_1_3⁵ + c_1_2·c_1_3⁴ + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2³·c_1_3
       + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2²·c_1_3 + c_1_0²·c_1_3³
       + c_1_0²·c_1_2·c_1_3², an element of degree 5
20. b_5_18 → c_1_2³·c_1_3² + c_1_2⁴·c_1_3 + c_1_1·c_1_2·c_1_3³ + c_1_1·c_1_2²·c_1_3²
       + c_1_1·c_1_2³·c_1_3 + c_1_1·c_1_2⁴ + c_1_1²·c_1_2·c_1_3² + c_1_1²·c_1_2³
       + c_1_0²·c_1_3³ + c_1_0²·c_1_2²·c_1_3, an element of degree 5
21. b_5_19 → c_1_2·c_1_3⁴ + c_1_2²·c_1_3³ + c_1_2³·c_1_3² + c_1_2⁴·c_1_3
       + c_1_1·c_1_2²·c_1_3² + c_1_1·c_1_2³·c_1_3 + c_1_1²·c_1_2²·c_1_3
       + c_1_0²·c_1_2·c_1_3², an element of degree 5
22. a_6_7 → 0, an element of degree 6

About the group

Ring generators

Ring relations

Completion information

Restriction maps

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