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 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 language | English |
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Pages (from-to) | 623-650 |
Number of pages | 28 |
Journal | London Mathematical Society. Proceedings |
Volume | 112 |
Issue number | 4 |
DOIs | |
Publication status | Published - 5 Apr 2016 |
Keywords
- Automophisms
- soluble group
ASJC Scopus subject areas
- Algebra and Number Theory