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




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