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dc.contributor.authorDetomi, Eloisa
dc.contributor.authorLucchini, Andrea
dc.contributor.authorRoney-Dougal, C.M.
dc.date.accessioned2015-12-12T00:11:57Z
dc.date.available2015-12-12T00:11:57Z
dc.date.issued2015-08
dc.identifier161270296
dc.identifier7a2f0dbf-8fd7-4e6d-97b3-3eb9b4e69067
dc.identifier000351979000021
dc.identifier84925335716
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 . https://doi.org/10.1016/j.jpaa.2014.12.005en
dc.identifier.issn0022-4049
dc.identifier.otherORCID: /0000-0002-0532-3349/work/73700933
dc.identifier.urihttps://hdl.handle.net/10023/7910
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.format.extent13
dc.format.extent230683
dc.language.isoeng
dc.relation.ispartofJournal of Pure and Applied Algebraen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectBDCen
dc.subject.lccQAen
dc.titleCoprime invariable generation and minimal-exponent groupsen
dc.typeJournal articleen
dc.contributor.sponsorEPSRCen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doi10.1016/j.jpaa.2014.12.005
dc.description.statusPeer revieweden
dc.date.embargoedUntil2016-08-01
dc.identifier.grantnumberEP/I03582X/1en


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