Complementation in Finite Groups

Abstract

If somebody wants to show what makes the difference between the theory of groups in general and the theory of finite groups in particular what makes as it were the theory of finite groups tick, then I would not know of any better way of showing this than by producing the following proof of the useful THEOREM OF SCHMIDT & IWASAWA : If every proper subgroup of the finite group G is nilpotent, then G is soluble.