David J. Green

Cohomology
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Cohomology of group number 2 of order 8

About the group

Ring generators

Ring relations

Back to groups of order 8

General information on the group

• The group has 2 minimal generators and exponent 4.
• It is abelian, isomorphic to C₂×C₄.

Structure of the cohomology ring

General information

• The cohomology ring is of dimension 2 and depth 2.
• The Poincaré series is

  1

  (t  −  1)2

• The a-invariants are -∞,-∞,-2.

About the group

Ring generators

Ring relations

Back to groups of order 8

Ring generators

The cohomology ring has 3 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_2_2, an element of degree 2

About the group

Ring generators

Ring relations

Back to groups of order 8

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 8