Automorphisms of soluble groups

Paul Flavell

doi:10.1112/plms/pdw005

Automorphisms of soluble groups

Paul Flavell

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

210 Downloads (Pure)

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, C_G(R) acts on C_V(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
Pages (from-to)	623-650
Number of pages	28
Journal	London Mathematical Society. Proceedings
Volume	112
Issue number	4
DOIs	https://doi.org/10.1112/plms/pdw005
Publication status	Published - 5 Apr 2016

Keywords

Automophisms
soluble group

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/plms/pdw005

FlavellP2016Automorphisms
Paul Flavell. Automorphisms of soluble groups. Proc. London Math. Soc. (2016) 112 (4): 623-650. doi:10.1112/plms/pdw005 © 2016 London Mathematical Society Accepted author manuscript deposited.
Accepted author manuscript, 444 KBLicence: None: All rights reserved

Cite this

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N2 - 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.

AB - 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.

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KW - soluble group

U2 - 10.1112/plms/pdw005

DO - 10.1112/plms/pdw005

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EP - 650

JO - London Mathematical Society. Proceedings

JF - London Mathematical Society. Proceedings

IS - 4

ER -

Automorphisms of soluble groups

Abstract

Keywords

ASJC Scopus subject areas

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