Cohomology of group number 1 of order 8

About the group Ring generators Ring relations Back to groups of order 8

General information on the group

  • The group has 1 minimal generators and exponent 8.
  • It is abelian, isomorphic to C8.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 1 and depth 1.
  • The Poincaré series is
     − 1
    t  −  1
  • The a-invariants are -∞,-1.

About the group Ring generators Ring relations Back to groups of order 8

Ring generators

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

  1. c_1_0, an element of degree 1
  2. c_2_0, 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


Simon A. King David J. Green
Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2 Ernst-Abbe-Platz 2
D-07743 Jena D-07743 Jena
Germany Germany
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46184
Fax: +49 (0)3641 9-46162
Office: Zi. 3524, Ernst-Abbe-Platz 2
E-mail: david dot green at uni hyphen jena dot de
Tel: +49 3641 9-46166
Fax: +49 3641 9-46162
Office: Zi 3512, Ernst-Abbe-Platz 2

Last change: 25.08.2009