Signs on group Latin squares
type: Item
instance of: scholarly article
title: Signs on group Latin squares
zbMATH Open document ID: 0857.05014
author: Alberto Marini
author: Giuseppe Pirillo
published in: Advances in Applied Mathematics
publication date: 1997-03-12T00:00:00Z
review text: Each row and column of a Latin square, \(L\), of order \(n\) can be thought of as a permutation of the elements of an \(n\)-set. For \(L\), associate \(rc\in \{++,+-,-+,--\}\) where \(r\) (respectively \(c\)) is \(+\) if \(L\) has an even number of rows (respectively columns) that are odd permutations, and where \(r\) (respectively \(c\)) is \(-\) if \(L\) has an odd number of rows (respectively columns) that are odd permutations. In this paper, the authors study group Latin squares (obtained from the Cayley table of a finite group, \(G\)). The ordering of the elements does not affect the row or column signs. Among other results, the authors show that if \(|G|\equiv 2\pmod 4\) then \(rc=--\), otherwise \(rc=++\).
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 922446
zbMATH Keywords: transformation group
zbMATH Keywords: odd permutations
zbMATH Keywords: group Latin squares
zbMATH Keywords: signs
reviewed by: Chester J. Salwach
MaRDI profile type: Publication
full work available at URL: aama.1996.0006
OpenAlex ID: W2057357652
DOI: 10.1006/AAMA.1996.0006
Recommended article: Signs on Latin squares
Recommended article: Orthogonal Latin squares based on groups
Recommended article: Q3829559
Recommended article: Alternating groups and Latin squares
Recommended article: Q3323967
Recommended article: Q3469110
Recommended article: Latin squares over Abelian groups
Recommended article: Latin squares over quasigroups
description: scientific article; zbMATH DE number 922446