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dc.contributor.authorRoney-Dougal, Colva Mary
dc.contributor.editorDabrowski, Konrad K.
dc.contributor.editorGadouleau, Maximillien
dc.contributor.editorGeorgiou, Nicholas
dc.contributor.editorJohnson, Matthew
dc.contributor.editorMertzios, George B.
dc.contributor.editorPaulusma, Daniël
dc.identifier.citationRoney-Dougal , C M 2021 , Maximal subgroups of finite simple groups : classifications and applications . in K K Dabrowski , M Gadouleau , N Georgiou , M Johnson , G B Mertzios & D Paulusma (eds) , Surveys in Combinatorics 2021 . London Mathematical Society Lecture Note Series , vol. 470 , Cambridge University Press , pp. 343-370 .
dc.identifier.otherPURE: 271737619
dc.identifier.otherPURE UUID: 4f90f13a-d1b1-4950-9de8-1b7784268311
dc.identifier.otherORCID: /0000-0002-0532-3349/work/98487621
dc.description.abstractThis paper surveys what is currently known about the maximal subgroups of the finite simple groups. After briefly introducing the groups themselves, if their maximal subgroups are completely determined then we present this classification. For the remaining finite simple groups our current knowledge is only partial: we describe the state of play, as well as giving some results that apply more generally. We also direct the reader towards computational resources for the construction of maximal subgroups. After this, we present three sample applications, selected because they combine group theoretical and combinatorial arguments, and because they use either or both of the detailed classifications and the looser statements that can be made about all maximal subgroups. In particu- lar, we discuss results relating to generation, and the generating graph; results concerning bases; and some applications to computational com- plexity, in particular to graph colouring and other problems with no known polynomial-time solution.
dc.publisherCambridge University Press
dc.relation.ispartofSurveys in Combinatorics 2021en
dc.relation.ispartofseriesLondon Mathematical Society Lecture Note Seriesen
dc.rightsCopyright © 2017, Cambridge University Press. 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.subjectQA Mathematicsen
dc.titleMaximal subgroups of finite simple groups : classifications and applicationsen
dc.typeConference itemen
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.St Andrews GAP Centreen

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