Jordan-Hölder theorem for pseudo-symmetric sets
type: Item
instance of: scholarly article
title: Jordan-Hölder theorem for pseudo-symmetric sets
zbMATH Open document ID: 0609.20002
author: Nobuo Nobusawa
published in: Osaka Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A pseudo-symmetric set is a pair (\({\mathcal U},\sigma)\) where \({\mathcal U}\) is a set and \(\sigma\) is a mapping of \({\mathcal U}\) into the group of permutations on \({\mathcal U}\) such that \(u^{\sigma (u)}=u\) for every \(u\in {\mathcal U}\) and \(\sigma (u^{\sigma (v)})=\sigma (v)^{-1}\sigma (u)\sigma (v)\) for u,v\(\in {\mathcal U}\). In this paper the author establishes an analogue of the Jordan-Hölder theorem in group theory for pseudo-symmetric sets.
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20N99
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 3985482
zbMATH Keywords: group of permutations
zbMATH Keywords: Jordan-Hölder theorem
zbMATH Keywords: pseudo-symmetric sets
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3985482