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OverviewThe author extends results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular he determines the maximal subgroups of this form. He also determines the maximal overgroups of short root subgroups in finite classical groups and the maximal overgroups in finite orthogonal groups of c-root subgroups. Full Product DetailsAuthor: Michael AschbacherPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.292kg ISBN: 9781470418458ISBN 10: 1470418452 Pages: 184 Publication Date: 30 April 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction 3-transpositions The $(V,f)$-setup Direct sum decompositions Subfield structures Modules for alternating groups Modules with $p=2$ The orthogonal space $\mathbf{F}_2^n$ Overgroups of long root subgroups Maximal overgroups of long root subgroups Subgroups containing long root elements Overgroups of short root subgroups Short root subgroups in symplectic groups of characteristic 2 Overgroups of subgroups in $\mathbf{R}_c$ in III Overgroups of subgroups in $\mathbf{R}_c$ in III when $q>3$ A special case for $q=3$ in III Overgroups of subgroups in $\mathbf{R}_c$ in III when $q=3$ A result of Stellmacher More case III with $q=3$ The proof of Theorem 1 A characterization of alternating groups Orthogonal groups with $q=2$ The proof of Theorem 2 Symplectic and unitary groups Symplectic and unitary groups with $q$ odd The proof of Theorem 3 Unitary groups with $q$ even The proofs of Theorems A and B ReferencesReviewsAuthor InformationMichael Aschbacher, Caltech, Pasadena, CA, USA. Tab Content 6Author Website:Countries AvailableAll regions |
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