2-Minimal subgroups of monomial, linear and unitary groups

Chris Parker, Peter Rowley

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Abstract

This paper gives a detailed and explicit description of all the 2- minimal subgroups for the finite linear and unitary groups defined over fields of odd characteristic. Also the 2-minimal subgroups of all the subgroups of these groups which contain the special linear and special unitary subgroups are described. For a finite group G, a subgroup P of G is 2-minimal if B < P, where B = NG(S) for some Sylow 2-subgroup S of G, and B is contained in a unique maximal subgroup of P. The 2-minimal subgroups of certain monomial groups, which play an important role in this work, are also determined.
Original languageEnglish
Pages (from-to)1-53
JournalJournal of Algebra
Volume543
Early online date8 Oct 2019
DOIs
Publication statusPublished - 1 Feb 2020

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