Cohomology of group number 1 of order 625

About the group Ring generators Ring relations Back to groups of order 625

General information on the group

  • The group has 1 minimal generators and exponent 625.
  • It is abelian, isomorphic to C625.

Structure of the cohomology ring

The Poincaré series is
 − 1
t  −  1

About the group Ring generators Ring relations Back to groups of order 625

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 625

Ring relations

There is one "obvious" relation:
   c_1_02

Apart from that, there are no relations.

About the group Ring generators Ring relations Back to groups of order 625


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