2-minimal subgroups of orthogonal groups

For a finite group G, a subgroup P of G is 2-minimal if B < P, where B = N-G(S) for some Sylow 2-subgroup S of G, and B is contained in a unique maximal subgroup of P. For fields of odd characteristic, this paper contains a detailed and explicit description of all the 2-minimal subgroups of the finite general orthogonal groups, and certain of their subgroups. Crown Copyright (c) 2021 Published by Elsevier Inc. All rights reserved.