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dc.contributor.authorBailey, R. A.
dc.contributor.authorCameron, Peter J.
dc.contributor.authorGiudici, Michael
dc.contributor.authorRoyle, Gordon F.
dc.identifier.citationBailey , R A , Cameron , P J , Giudici , M & Royle , G F 2021 , ' Groups generated by derangements ' , Journal of Algebra , vol. 572 , pp. 245-262 .
dc.identifier.otherPURE: 271788526
dc.identifier.otherPURE UUID: f57837ec-428f-4feb-b748-1415297f7e6e
dc.identifier.otherORCID: /0000-0003-3130-9505/work/86538145
dc.identifier.otherORCID: /0000-0002-8990-2099/work/86538148
dc.identifier.otherScopus: 85099225624
dc.identifier.otherWOS: 000614814500011
dc.descriptionFunding: the research of the last two authors is supported by the Australian Research Council Discovery Project DP200101951. This work was supported by EPSRC grant no EP/R014604/1. In addition, the second author was supported by a Simons Fellowship.en
dc.description.abstractWe examine the subgroup D(G) of a transitive permutation group G which is generated by the derangements in G. Our main results bound the index of this subgroup: we conjecture that, if G has degree n and is not a Frobenius group, then |G:D(G)|≤ √n-1; we prove this except when G is a primitive affine group. For affine groups, we translate our conjecture into an equivalent form regarding |H:R(H)|, where H is a linear group on a finite vector space and R(H) is the subgroup of H generated by elements having eigenvalue 1. If G is a Frobenius group, then D(G) is the Frobenius kernel, and so G/D(G) is isomorphic to a Frobenius complement. We give some examples where D(G) ≠ G, and examine the group-theoretic structure of G/D(G); in particular, we construct groups G in which G/D(G) is not a Frobenius complement.
dc.relation.ispartofJournal of Algebraen
dc.rightsCopyright © 2020 Elsevier Inc. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at
dc.subjectPermutation groupen
dc.subjectFrobenius groupen
dc.subjectLinear groupen
dc.subjectQA Mathematicsen
dc.titleGroups generated by derangementsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.description.statusPeer revieweden

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