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dc.contributor.authorDoostie, H.
dc.contributor.authorCampbell, P.P.
dc.identifier.citationDoostie , H & Campbell , P P 2006 , ' On the commutator lengths of certain classes of finitely presented groups ' , International Journal of Mathematics and Mathematical Sciences , vol. 2006 , 74981 .
dc.identifier.otherPURE: 116545106
dc.identifier.otherPURE UUID: f9c3224a-36d8-49de-b845-f78d3342a7da
dc.identifier.otherScopus: 33749513941
dc.description.abstractFor a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G - {1}}. The well-known commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) and by using this inequality we give upper bounds for the commutator lengths of certain classes of finite groups. In some cases these upper bounds involve the interesting sequences of Fibonacci and Lucas numbers.
dc.relation.ispartofInternational Journal of Mathematics and Mathematical Sciencesen
dc.rights© 2006 Doostie et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.en
dc.subjectQA Mathematicsen
dc.titleOn the commutator lengths of certain classes of finitely presented groupsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews.School of Mathematics and Statisticsen
dc.description.statusPeer revieweden

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