David J. Green

Cohomology
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Cohomology of group number 11 of order 625

About the group

Ring generators

Ring relations

Back to groups of order 625

General information on the group

• The group has 3 minimal generators and exponent 25.
• It is abelian, isomorphic to C₅×C₅×C₂₅.

Structure of the cohomology ring

The Poincaré series is

− 1

(t  −  1)3

About the group

Ring generators

Ring relations

Back to groups of order 625

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_2_3, an element of degree 2
5. c_2_4, an element of degree 2
6. c_2_5, an element of degree 2

About the group

Ring generators

Ring relations

Back to groups of order 625

Ring relations

There are 3 "obvious" relations:
   c_1_0², c_1_1², c_1_2²

Apart from that, there are no relations.

About the group

Ring generators

Ring relations

Back to groups of order 625