Show simple item record

Files in this item


Item metadata

dc.contributor.authorQuick, Martyn
dc.contributor.authorRuskuc, Nik
dc.identifier.citationQuick , M & Ruskuc , N 2010 , ' Growth of generating sets for direct powers of classical algebraic structures ' , Journal of the Australian Mathematical Society , vol. 89 , no. 1 , pp. 105-126 .
dc.identifier.otherPURE: 4157457
dc.identifier.otherPURE UUID: 0f9f7c81-d079-4595-9b3c-93808bc979fc
dc.identifier.otherScopus: 78049256325
dc.identifier.otherWOS: 000283959400008
dc.identifier.otherORCID: /0000-0002-5227-2994/work/58054909
dc.identifier.otherORCID: /0000-0003-2415-9334/work/73702033
dc.description.abstractFor an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the sequence d(A) when A is one of the classical structures—a group, ring, module, algebra or Lie algebra. We show that if A is finite then d(A) grows either linearly or logarithmically. In the infinite case constant growth becomes another possibility; in particular, if A is an infinite simple structure belonging to one of the above classes then d(A) is eventually constant. Where appropriate we frame our exposition within the general theory of congruence permutable varieties.
dc.relation.ispartofJournal of the Australian Mathematical Societyen
dc.rights(c) 2010 Australian Mathematical Publishing Association Inc.en
dc.subjectGenerating setsen
dc.subjectDirect productsen
dc.subjectAlgebraic structuresen
dc.subjectUniversal algebraen
dc.subjectQA Mathematicsen
dc.titleGrowth of generating sets for direct powers of classical algebraic structuresen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

This item appears in the following Collection(s)

Show simple item record