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dc.contributor.authorDetomi, Eloisa
dc.contributor.authorLucchini, Andrea
dc.contributor.authorRoney-Dougal, C.M.
dc.identifier.citationDetomi , E , Lucchini , A & Roney-Dougal , C M 2015 , ' Coprime invariable generation and minimal-exponent groups ' , Journal of Pure and Applied Algebra , vol. 219 , no. 8 , pp. 3453-3465 .
dc.identifier.otherPURE: 161270296
dc.identifier.otherPURE UUID: 7a2f0dbf-8fd7-4e6d-97b3-3eb9b4e69067
dc.identifier.otherWOS: 000351979000021
dc.identifier.otherScopus: 84925335716
dc.identifier.otherORCID: /0000-0002-0532-3349/work/73700933
dc.descriptionColva Roney-Dougal acknowledges the support of EPSRC grant EP/I03582X/1.en
dc.description.abstractA finite group G is coprimely invariably generated if there exists a set of generators {g1,. .,gu} of G with the property that the orders |g1|,. .,|gu| are pairwise coprime and that for all x1,. .,xu∈G the set {g1x1,. .,guxu} generates G. We show that if G is coprimely invariably generated, then G can be generated with three elements, or two if G is soluble, and that G has zero presentation rank. As a corollary, we show that if G is any finite group such that no proper subgroup has the same exponent as G, then G has zero presentation rank. Furthermore, we show that every finite simple group is coprimely invariably generated by two elements, except for O8+(2) which requires three elements. Along the way, we show that for each finite simple group S, and for each partition π1,. .,πu of the primes dividing |S|, the product of the number kπi(S) of conjugacy classes of πi-elements satisfies. ∏i=1u kπi(S)≤|S|/2|OutS|.
dc.relation.ispartofJournal of Pure and Applied Algebraen
dc.rightsCopyright © 2014. Elsevier Inc. All rights reserved. This is the author’s version of a work that was accepted for publication in Journal of Pure and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Pure and Applied Mathematics, 12 December 2014
dc.subjectQA Mathematicsen
dc.titleCoprime invariable generation and minimal-exponent groupsen
dc.typeJournal articleen
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

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