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A note on the probability of generating alternating or symmetric groups

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dc.contributor.authorMorgan, Luke
dc.contributor.authorRoney-Dougal, Colva Mary
dc.date.accessioned2016-08-21T23:34:18Z
dc.date.available2016-08-21T23:34:18Z
dc.date.issued2015-09
dc.identifier.citationMorgan , L & Roney-Dougal , C M 2015 , ' A note on the probability of generating alternating or symmetric groups ' , Archiv der Mathematik , vol. 105 , no. 3 , pp. 201-204 . https://doi.org/10.1007/s00013-015-0796-8en
dc.identifier.issn0003-889X
dc.identifier.otherPURE: 223509214
dc.identifier.otherPURE UUID: 45c65754-0e87-4df3-a991-1fc5d974ce52
dc.identifier.otherScopus: 84940589052
dc.identifier.otherWOS: 000360507900001
dc.identifier.otherORCID: /0000-0002-0532-3349/work/73700915
dc.identifier.urihttps://hdl.handle.net/10023/9348
dc.descriptionThe research of the first author is supported by the Australian Research Council grant DP120100446.en
dc.description.abstractWe improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.
dc.format.extent4
dc.language.isoeng
dc.relation.ispartofArchiv der Mathematiken
dc.rights© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at http://link.springer.com/article/10.1007/s00013-015-0796-8en
dc.subjectSymmetric groupen
dc.subjectAlternating groupen
dc.subjectGenerationen
dc.subjectProbabilityen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleA note on the probability of generating alternating or symmetric groupsen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.1007/s00013-015-0796-8
dc.description.statusPeer revieweden
dc.date.embargoedUntil2016-08-21


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