On minimal \(p\)-degrees in \(2\)-transitive permutation groups
type: Item
instance of: scholarly article
title: On minimal \(p\)-degrees in \(2\)-transitive permutation groups
zbMATH Open document ID: 0944.20002
author: Jens Höchsmann
published in: Archiv der Mathematik
publication date: 2000-02-15T00:00:00Z
review text: If \(G\) is a transitive permutation group on a finite set \(\Omega\) of size \(n\) and if \(p\) is a prime divisor of \(|G|\), the minimal \(p\)-degree of \(G\), denote by \(m_p(G)\), is the smallest number of points moved by a non-identity \(p\)-element of \(G\). This is a generalization of the notion of minimal degree \(m(G)\) (the smallest number of points moved by any non-identity element), since \(m(G)=m_p(G)\) for a suitable prime divisor \(p\) of \(|G|\). Using the classification of finite 2-transitive permutation groups, the author shows that \(m_p(G)\geq\tfrac{p-1}{p+1}\cdot|\Omega|\) if \(G\) is 2-transitive and \(\text{Alt}(\Omega)\not\leq G\). All cases where \(m_p(G)<\tfrac{p-1}p\cdot|\Omega|\) are identified and minimal \(p\)-degrees are calculated for various 2-transitive permutation groups.
Mathematics Subject Classification ID: 20B20
Mathematics Subject Classification ID: 20B05
zbMATH DE Number: 1333328
zbMATH Keywords: finite 2-transitive permutation groups
zbMATH Keywords: minimal \(p\)-degrees
reviewed by: Alice Devillers
MaRDI profile type: Publication
full work available at URL: s000130050349
OpenAlex ID: W1973111229
DOI: 10.1007/S000130050349
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description: scientific article; zbMATH DE number 1333328