Mathematics:

Cohomology
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Jena:

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David Green

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Singular

Gap

Cohomology of group number 2301 of order 128

About the group

Ring generators

Ring relations

Back to groups of order 128

General information on the group

• The group has 5 minimal generators and exponent 8.
• It is abelian, isomorphic to C₂×C₂×C₂×C₂×C₈.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 5 and depth 5.
• The Poincaré series is

  − 1

  (t  −  1)5

• The a-invariants are -∞,-∞,-∞,-∞,-∞,-5.

About the group

Ring generators

Ring relations

Back to groups of order 128

Ring generators

The cohomology ring has 6 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_1_4, an element of degree 1
6. c_2_14, an element of degree 2

About the group

Ring generators

Ring relations

Back to groups of order 128

Ring relations

There is one minimal relation of degree 2:

1. c_1_0²

About the group

Ring generators

Ring relations

Back to groups of order 128