Groups with anti-symmetric mappings
type: Item
instance of: scholarly article
title: Groups with anti-symmetric mappings
zbMATH Open document ID: 0832.20039
DOI: 10.1007/BF01195537
author: Joseph A. Gallian
author: Matthew D. Mullin
published in: Archiv der Mathematik
publication date: 1996-02-25T00:00:00Z
review text: We call a permutation \(\phi\) from a group to itself anti-symmetric if \(\phi(x)y = \phi(y)x\) implies that \(x = y\). Any anti-symmetric mapping of a group \(G\) can be used to assign a check digit to any string of characters from \(G\) so that all single errors and all transposition errors of adjacent characters are detected. When \(G\) is Abelian, anti-symmetric mappings are equivalent to the much studied complete mappings. In this paper we determine large classes of important groups that have anti-symmetric mappings and classes that do not. In particular, all finite simple groups except \(Z_2\) have anti-symmetric mappings. We also establish some general criteria for the existence of anti-symmetric mappings.
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 94B60
zbMATH DE Number: 815690
zbMATH Keywords: anti-symmetric mappings
zbMATH Keywords: complete mappings
zbMATH Keywords: finite simple groups
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01195537
OpenAlex ID: W2058940670
description: scientific article; zbMATH DE number 815690