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dc.contributor.authorHolt, Derek
dc.contributor.authorRoney-Dougal, Colva Mary
dc.identifier.citationHolt , D & Roney-Dougal , C M 2013 , ' Minimal and random generation of permutation and matrix groups ' , Journal of Algebra , vol. 387 , pp. 195-214 .
dc.identifier.otherPURE: 5157201
dc.identifier.otherPURE UUID: acddc0fe-c53d-4ce2-a60b-afd74e9a58c0
dc.identifier.otherScopus: 84877841197
dc.identifier.otherWOS: 000320090300012
dc.identifier.otherORCID: /0000-0002-0532-3349/work/73700916
dc.description.abstractWe prove explicit bounds on the numbers of elements needed to generate various types of finite permutation groups and finite completely reducible matrix groups, and present examples to show that they are sharp in all cases. The bounds are linear in the degree of the permutation or matrix group in general, and logarithmic when the group is primitive. They can be combined with results of Lubotzky to produce explicit bounds on the number of random elements required to generate these groups with a specified probability. These results have important applications to computational group theory. Our proofs are inductive and largely theoretical, but we use computer calculations to establish the bounds in a number of specific small cases.
dc.relation.ispartofJournal of Algebraen
dc.rights© 2013 Elsevier Inc. This is the author’s version of a work that was accepted for publication in the Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, Vol 387, 2013. DOI:
dc.subjectFinite groupsen
dc.subjectGeneration of groupsen
dc.subjectMatrix groupsen
dc.subjectPermutation groupsen
dc.subjectProbabilistic and symptotic group theoryen
dc.subjectQA Mathematicsen
dc.titleMinimal and random generation of permutation and matrix groupsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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