On the existence of \(k\)-tournaments with given automorphism group
type: Item
instance of: scholarly article
title: On the existence of \(k\)-tournaments with given automorphism group
zbMATH Open document ID: 0864.05043
DOI: 10.1016/0012-365X(95)00351-V
published in: Discrete Mathematics
publication date: 1997-06-22T00:00:00Z
review text: A \(k\)-tournament \(T\) on \(n\) vertices consists of an \(n\)-set \(V(T)\) of vertices and the \({n\choose k}\)-collection of \(k\)-subsets of \(V(T)\), where each \(k\)-subset has been assigned one of the \(k!\) possible linear orders. The main result of this lucid paper is that, for any finite group \(G\) and any integer \(k\geq 3\), there exists a \(k\)-tournament whose automorphism group is isomorphic to \(G\) if and only if \(|G|\) and \(k\) are relatively prime. This extends a result of \textit{J. W. Moon} [Can. J. Math. 16, 485-489 (1964; Zbl 0121.40204)] that a finite group is isomorphic to the automorphism group of a tournament (i.e., a 2-tournament) if and only if its order is odd.
reviewed by: Mark E. Watkins
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 897582
zbMATH Keywords: \(k\)-tournament
zbMATH Keywords: automorphism group
zbMATH Keywords: tournament
author: Susan Marshall
MaRDI profile type: Publication
cites work: Q3929778
cites work: Tournaments with given (infinite) automorphism group
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cites work: Q4032987
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cites work: Q3680857
Wikidata QID: Q127370925
full work available at URL: 0012-365x(95)00351-v
OpenAlex ID: W2056116373
description: scientific article; zbMATH DE number 897582