{"title":"Transitive permutation groups with elements of movement m or m − 2","authors":"M. Alaeiyan, Murtadha Shabeeb, M. Akbarizadeh","doi":"10.15672/hujms.1223815","DOIUrl":null,"url":null,"abstract":"Let G be a permutation group on a set \\Omega with no fixed points in \\Omega and let m be a positive integer. \nIf for each subset \\Gamma of \\Omegga the size |\\Gamma^g \\ Gamma| is bounded, for g in G, we define the \nmovement of g as the max |\\Gamma^g \\ Gamma| over all subsets \\Gamma of \\Omega, and the movement \nof G is defined as the maximum of move(g) over all non-identity elements of g in G. In this paper we classify all \ntransitive permutation groups with bounded movement equal tomthat are not a 2-group, but in which every \nnon-identity element has movement m or m − 2.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1223815","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let G be a permutation group on a set \Omega with no fixed points in \Omega and let m be a positive integer.
If for each subset \Gamma of \Omegga the size |\Gamma^g \ Gamma| is bounded, for g in G, we define the
movement of g as the max |\Gamma^g \ Gamma| over all subsets \Gamma of \Omega, and the movement
of G is defined as the maximum of move(g) over all non-identity elements of g in G. In this paper we classify all
transitive permutation groups with bounded movement equal tomthat are not a 2-group, but in which every
non-identity element has movement m or m − 2.
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