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Coprime invariable generation and minimal-exponent groups
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dc.contributor.author | Detomi, Eloisa | |
dc.contributor.author | Lucchini, Andrea | |
dc.contributor.author | Roney-Dougal, C.M. | |
dc.date.accessioned | 2015-12-12T00:11:57Z | |
dc.date.available | 2015-12-12T00:11:57Z | |
dc.date.issued | 2015-08 | |
dc.identifier | 161270296 | |
dc.identifier | 7a2f0dbf-8fd7-4e6d-97b3-3eb9b4e69067 | |
dc.identifier | 000351979000021 | |
dc.identifier | 84925335716 | |
dc.identifier.citation | Detomi , 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.2014.12.005 | en |
dc.identifier.issn | 0022-4049 | |
dc.identifier.other | ORCID: /0000-0002-0532-3349/work/73700933 | |
dc.identifier.uri | https://hdl.handle.net/10023/7910 | |
dc.description | Colva Roney-Dougal acknowledges the support of EPSRC grant EP/I03582X/1. | en |
dc.description.abstract | A 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.extent | 13 | |
dc.format.extent | 230683 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Pure and Applied Algebra | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | Coprime invariable generation and minimal-exponent groups | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1016/j.jpaa.2014.12.005 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2016-08-01 | |
dc.identifier.grantnumber | EP/I03582X/1 | en |
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