Solvable 2-local subgroups of finite groups (Q790241)

The main result of the paper under review is the following Theorem. Let G be a finite simple group of characteristic 2 type and H be a maximal 2- local subgroup of G. Suppose that H is solvable and the 2-rank of \(O_ 2(H)\) is at most 3. Then G is isomorphic to one of the following groups: \(L_ 2(2^ n\pm 1)\), \(L_ 2(8)\), \(L_ 3(3)\), \(PSp_ 4(3)\), \(U_ 3(3)\), \(U_ 3(4)\), \(U_ 3(8)\), \(U_ 4(3)\), \(U_ 5(2)\), Sz(8), \(G_ 2(3)\), \(M_{11}\). In a previous paper of the author [Algebra Logika 21, 178-192 (1982; Zbl 0507.20012)] the case of nonsolvable H was considered.