Automorphisms and enumeration of switching classes of tournaments
type: Item
instance of: scholarly article
title: Automorphisms and enumeration of switching classes of tournaments
zbMATH Open document ID: 0956.05050
author: Peter J. Cameron
author: László Babai
published in: The Electronic Journal of Combinatorics
publication date: 2000-09-14T00:00:00Z
full work available at URL: https://eudml.org/doc/120808
full work available at URL: v7i1r38.html
review text: In this paper the operation of switching of tournaments is investigated. The main result is Theorem 5.2. A finite group is the automorphism group of some switching class of tournaments if and only if its Sylow 2-subgroups are cyclic or dihedral. It is a simple corollary that if \(G\) has cyclic or dihedral Sylow 2-subgroups then there is a switching class \(C\) of tournaments, with Aut(\(C)\simeq G\), having the property that every subgroup of \(G\) of odd order is the full automorphism group of a tournament in \(C\) (Corollary 6.10).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05E99
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 1498627
zbMATH Keywords: switching classes
zbMATH Keywords: tournaments
zbMATH Keywords: automorphism group
reviewed by: Alexandre A. Makhnev
describes a project that uses: OEIS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1498627