Second class of maximal subgroups in finite classical groups (Q1821201)

Let G be a finite group of Lie type over a finite field \(F_ q\) and (B,N) be its split BN-pair. Let H denote the subgroup \(B\cap N\). In a previous paper [ibid. 106, 536-542 (1987; Zbl 0609.20029)] the author described maximal subgroups in some classical groups G containing N. In this paper the author determines maximal subgroups in G containing H but not containing N provided that G is isomorphic to one of the groups \(SL_ n(q)\), \(Sp_{2\ell}(q)\) or \(\Omega_{2\ell +1}(q)\), q is odd and \(q>11\) (or q is a suitable large power of 2). These maximal subgroups are reduced to some subgroups of the permutation group. The result of \textit{G. M. Seitz} [ibid. 61, 16-27 (1979; Zbl 0426.20036)] is used. Reviewer's remark: A more general result on maximal subgroups of G containing H is obtained by \textit{N. A. Vavilov} [Rings and modules. Limit theorems of probability theory, Vol. 1, Leningrad 1986, 65-75 (1987)].