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The probability of generating a finite simple group
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dc.contributor.author | Menezes, Nina Emma | |
dc.contributor.author | Quick, Martyn | |
dc.contributor.author | Roney-Dougal, Colva Mary | |
dc.date.accessioned | 2014-11-01T00:01:24Z | |
dc.date.available | 2014-11-01T00:01:24Z | |
dc.date.issued | 2013-11 | |
dc.identifier.citation | Menezes , N E , Quick , M & Roney-Dougal , C M 2013 , ' The probability of generating a finite simple group ' , Israel Journal of Mathematics , vol. 198 , no. 1 , pp. 371-392 . https://doi.org/10.1007/s11856-013-0034-7 | en |
dc.identifier.issn | 0021-2172 | |
dc.identifier.other | PURE: 21568887 | |
dc.identifier.other | PURE UUID: 3f978e41-cd84-4e84-84bd-1eb40cfd8f30 | |
dc.identifier.other | Scopus: 84883804352 | |
dc.identifier.other | ORCID: /0000-0002-5227-2994/work/58054905 | |
dc.identifier.other | ORCID: /0000-0002-0532-3349/work/73700913 | |
dc.identifier.uri | https://hdl.handle.net/10023/5658 | |
dc.description.abstract | We study the probability of generating a finite simple group, together with its generalisation PG,socG(d), the conditional probability of generating an almost simple finite group G by d elements, given that these elements generate G/ socG. We prove that PG,socG(2) ⩾ 53/90, with equality if and only if G is A6 or S6, and establish a similar result for PG,socG(3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results. | |
dc.format.extent | 22 | |
dc.language.iso | eng | |
dc.relation.ispartof | Israel Journal of Mathematics | en |
dc.rights | © 2013 The Hebrew University Magnes Press, Jerusalem. Published by Springer. The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-013-0034-7 | en |
dc.subject | Probability | en |
dc.subject | Finite simple group | en |
dc.subject | Direct products | en |
dc.subject | Profinite groups | en |
dc.subject | QA Mathematics | en |
dc.subject.lcc | QA | en |
dc.title | The probability of generating a finite simple group | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.sponsor | EPSRC | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. School of Mathematics and Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1007/s11856-013-0034-7 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2014-11-01 | |
dc.identifier.grantnumber | EP/H011978/1 | en |
dc.identifier.grantnumber | EP/I03582X/1 | en |
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