On the module structure of the mod p cohomology of a p-group
type: Item
instance of: scholarly article
title: On the module structure of the mod p cohomology of a p-group
zbMATH Open document ID: 0535.20029
DOI: 10.1007/BF01190949
author: Thomas Diethelm
author: Urs Stammbach
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: Let P be a finite p-group and let Q be a group acting faithfully on P. The paper studies the Q-module structure of the cohomology algebra \(H^*(P,k)\) where k denotes the field of p elements. The first author has shown that if Q is a p'-group then every simple kQ-module appears infinitely often as a direct summand of \(H^*(P,k)\). Here this result is generalized to arbitrary groups Q: There exists a number \(\ell\) such that for all \(m=0,1,2,...\) every simple kQ-module appears as a composition factor of \(\oplus^{\ell +m}_{i=m+1}H^{2i}(P,k).\) An upper bound for \(\ell\) is given in terms of P, Q and the operation of Q on P.
Mathematics Subject Classification ID: 20J06
zbMATH DE Number: 3849492
zbMATH Keywords: finite p-group
zbMATH Keywords: cohomology algebra
zbMATH Keywords: simple kQ-module
zbMATH Keywords: direct summand
MaRDI profile type: Publication
cites work: On the cohomology of groups of p-length 1
cites work: A Generalization of the Transfer Map in the Cohomology of Groups
cites work: Cohomology of Group Extensions
cites work: Q3958660
description: scientific article; zbMATH DE number 3849492