Generation of alternating groups by pairs of conjugates
type: Item
instance of: scholarly article
title: Generation of alternating groups by pairs of conjugates
zbMATH Open document ID: 0617.20045
DOI: 10.1007/BF01848100
author: J. L. Brenner
author: Leroy B. Beasley
author: Mihály Szalay
author: Alan G. Williamson
author: P. Erdős
published in: Periodica Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: Let \(A_n\) denote the alternating group of degree \(n\). The main result of the paper is the following Theorem 3.05. Almost all conjugacy classes of \(A_n\) contain a pair of generators. (In other words, the proportion of conjugacy classes in \(A_n\) that contain a pair of generators approaches 1 as \(n\to \infty.)\) The main theorem required the proof of the following Theorems 2.04 and 3.04. Let \(C\) be a conjugacy class (in the symmetric group of degree \(n\)) of type \(T=1^{e(1)}2^{e(2)}3^{e(3)}... \). If \(T\) is not the type of an involution, and if the relation \(\sum _{j\geq 1}e(j)\leq n/2\) holds, then \(C\) contains a pair of elements that generate a primitive group. Almost all partitions of n have a summand \(>1\) and relatively prime to the other summands.
Mathematics Subject Classification ID: 20P05
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20B35
Mathematics Subject Classification ID: 11N45
zbMATH DE Number: 4000235
zbMATH Keywords: alternating group
zbMATH Keywords: conjugacy classes
zbMATH Keywords: pair of generators
zbMATH Keywords: partitions
Wikidata QID: Q105675723
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01848100
OpenAlex ID: W1998243396
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description: scientific article; zbMATH DE number 4000235