Permutation groups, simple groups, and sieve methods
type: Item
instance of: scholarly article
title: Permutation groups, simple groups, and sieve methods
zbMATH Open document ID: 1091.11035
DOI: 10.1007/BF02775443
author: Cheryl E. Praeger
author: Aner Shalev
author: D. R. Heath-Brown
published in: Israel Journal of Mathematics
publication date: 2006-02-06T00:00:00Z
review text: Let \(I\) be the set of indices of non-trivial subgroups of finite non-abelian simple groups except that of the alternating group on \(n-1\) letters in the alternating group in \(n\) letters. In the paper under review for any real number \(x>1\) it is shown that the number of integers \(n\) in \(I\) not exceeding \(x\) is ~\(hx/\log(x)\) for some given constant \(h\). As a consequence it is shown that for most positive integers \(n\) the only quasiprimitive permutation groups of degree \(n\) are the symmetric and the alternating groups on \(n\) letters. The proof is a combination of group theoretic and number theoretic methods.
Mathematics Subject Classification ID: 11N45
Mathematics Subject Classification ID: 11N36
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 5003416
zbMATH Keywords: permutation group
zbMATH Keywords: simple group
zbMATH Keywords: Sieve method
Wikidata QID: Q56987849
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
cites work: Finite permutation groups with a transitive minimal normal subgroup
cites work: On the degrees of primitive permutation groups
cites work: Minimal degree for a permutation representation of a classical group
cites work: Q4520255
cites work: Q4882944
cites work: Q4052222
cites work: On the Overgroups of Irreducible Subgroups of the Finite Classical Groups
cites work: Q4015763
cites work: Cyclic Matrices Over Finite Fields
cites work: Bounds on finite quasiprimitive permutation groups
cites work: Q4293080
cites work: Q4004234
full work available at URL: https://doi.org/10.1007/bf02775443
OpenAlex ID: W2034018157
description: scientific article; zbMATH DE number 5003416