David J. Green

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Cohomology of group number 997 of order 128

About the group

Ring generators

Ring relations

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General information on the group

• The group has 4 minimal generators and exponent 4.
• It is abelian, isomorphic to C₂×C₄×C₄×C₄.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 4 and depth 4.
• The Poincaré series is

  1

  (t  −  1)4

• The a-invariants are -∞,-∞,-∞,-∞,-4.

About the group

Ring generators

Ring relations

Back to groups of order 128

Ring generators

The cohomology ring has 7 minimal generators of maximal degree 2:

1. c_1_0, an element of degree 1
2. c_1_1, an element of degree 1
3. c_1_2, an element of degree 1
4. c_1_3, an element of degree 1
5. c_2_7, an element of degree 2
6. c_2_8, an element of degree 2
7. c_2_9, an element of degree 2

About the group

Ring generators

Ring relations

Back to groups of order 128

Ring relations

There are 3 minimal relations of maximal degree 2:

1. c_1_0²
2. c_1_1²
3. c_1_2²

About the group

Ring generators

Ring relations

Back to groups of order 128