Automorphisms of soluble groups

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

Abstract

Let R be a group of prime order r that acts on the r-group G, let RG be the semidirect product of G with R, let F be a field and V be a faithful completely reducible F[RG]-module. Trivially, CG(R) acts on CV (R). Let K be the kernel of this action. What can be said about K? This question is considered when G is soluble. It turns out that K is subnormal in G or r is a Fermat or half-Fermat prime. In the latter cases, the subnormal closure of K in G is described. Several applications to the theory of automorphisms of soluble groups are given.

Details

Original languageEnglish
Pages (from-to)623
Number of pages650
JournalLondon Mathematical Society. Proceedings
Volume112
Issue number3
Publication statusPublished - 2016

Keywords

  • Automophisms, soluble group

ASJC Scopus subject areas