Generic fixed point free action of arbitrary finite groups
type: Item
instance of: scholarly article
title: Generic fixed point free action of arbitrary finite groups
zbMATH Open document ID: 0574.20013
DOI: 10.1007/BF01174184
author: Alexandre Turull
published in: Mathematische Zeitschrift
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173506
review text: Let A be a finite group acting on the solvable group G with the orders of A and G relatively prime and \(C_ G(A)\) trivial. If the action of A on G is ''generic'', a sharp bound is obtained for the Fitting height of G. The action of A on G is generic if for the action of all proper subgroups of A on sections of G there are ''enough regular orbits and modules''. It is known that if A is solvable then the Fitting height of G is bounded by the number of primes, counting multiplicities, that divide the order of A in certain special cases and in general by twice that number. The sharp bound obtained here for the case of an arbitrary finite group A whose action on G is generic is l(A), the largest integer n such that there exists a sequence \(1=S_ 0\subset S_ 1\subset S_ 2\subset...\subset S_ n=A\) of subgroups of A.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 3916545
zbMATH Keywords: solvable group
zbMATH Keywords: action
zbMATH Keywords: Fitting height
MaRDI profile type: Publication
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OpenAlex ID: W2037850019
description: scientific article; zbMATH DE number 3916545