Mathematics:

Cohomology
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Jena:

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David Green

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Singular

Gap

Cohomology of group number 988 of order 128

About the group

Ring generators

Ring relations

Back to groups of order 128

General information on the group

• The group has 3 minimal generators and exponent 32.
• It is abelian, isomorphic to C₂×C₂×C₃₂.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 3 and depth 3.
• The Poincaré series is

  − 1

  (t  −  1)3

• The a-invariants are -∞,-∞,-∞,-3.

About the group

Ring generators

Ring relations

Back to groups of order 128

Ring generators

The cohomology ring has 4 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_2_5, 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