A characteristic subgroup of a group of odd order
A characteristic subgroup of a group of odd order
In particular, if 2 £ π and G ^ 1, or if O 2 (G) ^ 1, then there exists a nonidentity characteristic subgroup of H that is a normal subgroup of G.COROLLARY.Assume the hypothesis of Theorem 2 and assume that 2,3 £ 7r.Then J{H) = J(F(G)).