Characterizations without characters (Q1173592)

The authors present an almost character-free proof of the following case of the dihedral theorem: Let \(G\) be a finite simple group with a dihedral Sylow 2-subgroup. Suppose that the centralizer \(H\) of an involution of \(G\) is properly contained in a subgroup \(\tilde H\) of \(G\) with \(F^*(\tilde H)=F(\tilde H)\). Then \(G\) is isomorphic to either \(A_ 5\), \(PSL(3,2)\), \(PSL(2,9)\) or \(A_ 7\).--\ In addition to that, they give a character-free proof of the following well-known result of Richard Brauer: Let \(G\) be a finite simple group with an involution t such that the centralizer in \(G\) of \(t\) is isomorphic to \(GL(2,3)\). Then \(G\) is isomorphic to \(M_{11}\) or \(PSL(3,3)\).--\ Jörg Hrabě de Angelis and the reviewer had also given a very detailed character-free proof of the latter theorem and distributed photocopies of it in 1989.