On fixed-point-free automorphisms

Glen Collins; Paul Flavell

doi:10.1016/j.jalgebra.2014.10.030

On fixed-point-free automorphisms

Glen Collins, Paul Flavell

Mathematics

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Abstract

Let R be a cyclic group of prime order which acts on the extraspecial group F in such a way that F=[F,R]. Suppose RF acts on a group G so that C_G(F)=1 and (|R|,|G|)=1. It is proved that F(C_G(R))⊆F(G). As corollaries to this, it is shown that the Fitting series of CG(R) coincides with the intersections of C_G(R) with the Fitting series of G , and that when |R| is not a Fermat prime, the Fitting heights of C_G(R) and G are equal.

Original language	English
Pages (from-to)	798-811
Journal	Journal of Algebra
Volume	423
Early online date	12 Nov 2014
DOIs	https://doi.org/10.1016/j.jalgebra.2014.10.030
Publication status	Published - 1 Feb 2015

Keywords

Automorphism
Fixed-point-free
Fitting height

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10.1016/j.jalgebra.2014.10.030

Collins_Flavell_On_fixed_point_free_automorphisms_Journal_Algebra_2015
Eligibility for repository : checked 13/11/2014
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http://linkinghub.elsevier.com/retrieve/pii/S0021869314006176

Cite this

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abstract = "Let R be a cyclic group of prime order which acts on the extraspecial group F in such a way that F=[F,R]. Suppose RF acts on a group G so that CG(F)=1 and (|R|,|G|)=1. It is proved that F(CG(R))⊆F(G). As corollaries to this, it is shown that the Fitting series of CG(R) coincides with the intersections of CG(R) with the Fitting series of G , and that when |R| is not a Fermat prime, the Fitting heights of CG(R) and G are equal.",

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AU - Flavell, Paul

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N2 - Let R be a cyclic group of prime order which acts on the extraspecial group F in such a way that F=[F,R]. Suppose RF acts on a group G so that CG(F)=1 and (|R|,|G|)=1. It is proved that F(CG(R))⊆F(G). As corollaries to this, it is shown that the Fitting series of CG(R) coincides with the intersections of CG(R) with the Fitting series of G , and that when |R| is not a Fermat prime, the Fitting heights of CG(R) and G are equal.

AB - Let R be a cyclic group of prime order which acts on the extraspecial group F in such a way that F=[F,R]. Suppose RF acts on a group G so that CG(F)=1 and (|R|,|G|)=1. It is proved that F(CG(R))⊆F(G). As corollaries to this, it is shown that the Fitting series of CG(R) coincides with the intersections of CG(R) with the Fitting series of G , and that when |R| is not a Fermat prime, the Fitting heights of CG(R) and G are equal.

KW - Automorphism

KW - Fixed-point-free

KW - Fitting height

U2 - 10.1016/j.jalgebra.2014.10.030

DO - 10.1016/j.jalgebra.2014.10.030

M3 - Article

SN - 0021-8693

VL - 423

SP - 798

EP - 811

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On fixed-point-free automorphisms

Abstract

Keywords

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