On the Cohomology of Central Frattini Extensions

Alejandro Adem and Jonathan Pakianathan

Mathematics Department
University of Wisconsin
Madison, Wisconsin, 53706 


Abstract

In this paper we provide calculations for the mod p cohomology
of certain p-groups, using topological methods.
More precisely, we look at p-groups G defined as central extensions
1-> V -> G ->W ->1 of elementary abelian groups
such that the mod p reduction of G/[G,G] is W and
the defining k-invariants span the entire image of the
Bockstein. We show that if p>dim V-dim W+1, then the mod p cohomology
of G can be explicitly computed as an algebra.