Automorphisms of soluble groups

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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 픽 be a field and V be a faithful completely reducible 픽[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.
Original languageEnglish
Pages (from-to)623-650
Number of pages28
JournalLondon Mathematical Society. Proceedings
Issue number4
Publication statusPublished - 5 Apr 2016


  • Automophisms
  • soluble group

ASJC Scopus subject areas

  • Algebra and Number Theory


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