Non-triviality of Tate cohomology for certain classes of finite p-groups

ABSTRACT

We prove that the Tate cohomology groups Ĥⁿ(G∕Φ(G),Z(Φ(G))) are non-trivial, whenever G is a finite p-group of class 3, or the pth term of the upper central series of G contains Z(Φ(G)). This confirms a conjecture of Schmid for these groups.

KEYWORDS:

• Finite p-groups
• group cohomology

MATHEMATICS SUBJECT CLASSIFICATION:

• 20D15
• 20J06

Acknowledgments

A part of this work was done while the second and the third authors were visiting the School of Mathematics, Institute for Research in Fundamental Sciences (IPM). These authors are grateful for the hospitality of all the people there.