Note on even tournaments whose automorphism groups contain regular subgroups
type: Item
instance of: scholarly article
title: Note on even tournaments whose automorphism groups contain regular subgroups
zbMATH Open document ID: 0773.05054
published in: Hokkaido Mathematical Journal
publication date: 1993-05-16T00:00:00Z
review text: A tournament \(A\) is defined to be the adjacency matrix of a complete asymmetric digraph. \(A\) is called even if the inner product of any two distinct row vectors of \(A\) is even. An automorphism of \(A\) is a permutation matrix \(P\) such that \(P^ tAP=A\). The multiplicative group \(G(A)\) of all automorphisms of \(A\) is called the automorphism group of \(A\). The main results are the following theorems. Theorem 1. If the order of 2 modulo every prime divisor of \(v\) is singly even, then there exists a tournament of order \(v\) whose automorphism group contains a regular subgroup which is isomorphic to an arbitrarily given group \(G\) of order \(v\). Theorem 2. If the order of 2 modulo every prime divisor of \(v\) is odd, then there exists an even tournament of order \(v\) whose automorphism group contains a regular subgroup which is isomorphic to an arbitrarily given group \(G\) of order \(v\).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 165212
zbMATH Keywords: tournament
zbMATH Keywords: adjacency matrix
zbMATH Keywords: permutation matrix
zbMATH Keywords: automorphism group
author: Noboru Ito
reviewed by: Ulrike Baumann
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381413126
OpenAlex ID: W2048945832
DOI: 10.14492/HOKMJ/1381413126
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description: scientific article; zbMATH DE number 165212