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dc.contributor.authorDetomi, Eloisa
dc.contributor.authorLucchini, Andrea
dc.contributor.authorRoney-Dougal, Colva Mary
dc.identifier.citationDetomi , E , Lucchini , A & Roney-Dougal , C M 2014 , ' On the probability of generating a monolithic group ' , Journal of Algebra , vol. 407 , pp. 413-433 .
dc.identifier.otherPURE: 114227981
dc.identifier.otherPURE UUID: 6546b556-b15f-44ac-ab18-ba2db4b1411e
dc.identifier.otherScopus: 84898800594
dc.identifier.otherWOS: 000335616600018
dc.identifier.otherORCID: /0000-0002-0532-3349/work/73700918
dc.descriptionThis research was supported through EPSRC grant EP/I03582X/1. The APC was paid through RCUK open access block grant funds.en
dc.description.abstractA group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By PL,N(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that PL,N(k) is controlled by PY,S(2), where N≅Sr and Y is a 2-generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information about PL,N(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.
dc.relation.ispartofJournal of Algebraen
dc.rightsCopyright 2014, the authors. This is an open access article under the CC-BY license.
dc.subjectFinite group theoryen
dc.subjectRandom generation of finite groupsen
dc.subjectFinite simple groupsen
dc.subjectCrown-based poweren
dc.subjectQA Mathematicsen
dc.titleOn the probability of generating a monolithic groupen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
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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