Classes of universal words for the infinite symmetric groups
type: Item
instance of: scholarly article
title: Classes of universal words for the infinite symmetric groups
zbMATH Open document ID: 0569.20005
DOI: 10.1007/BF01278598
author: Manfred Droste
published in: Algebra Universalis
publication date: 1985-01-01T00:00:00Z
review text: In the literature several authors have dealt with the problem of characterizing for various families Z of groups the set of all Z- universal words. The paper is devoted to this problem for the family ISym of all infinite symmetric groups \(S_{\nu}\) (\(\nu\geq 0)\), where \(S_{\nu}\) denotes the group of all permutations of a set of cardinality \(\aleph_{\nu}\). First, the generalization of earlier results is given. Next a new class of arbitrarily complex ISym-universal words is presented. The paper ends with a characterization of those simple factor- groups H in the Jordan-Hölder decomposition series of \(S_{\nu}\) which are verbally complete, i.e. in which any non-trivial word is H-universal.
reviewed by: M.Pałasiński
Mathematics Subject Classification ID: 20B30
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F10
zbMATH DE Number: 3908661
zbMATH Keywords: Z-universal words
zbMATH Keywords: infinite symmetric groups
zbMATH Keywords: ISym-universal words
zbMATH Keywords: simple factor-groups
zbMATH Keywords: Jordan-Hölder decomposition series
zbMATH Keywords: verbally complete
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3908661