关于极大子群指数的一个注记Ⅲ

A Note on Indices of Maximal Subgroups Ⅲ

作为Huppert定理的一个推广,陈重穆证明了:群G的每一个包含Sylow子群正规化子的极大子群在G内有素数指数,则群G超可解.不运用群G的可解性,本文给出了它为超可解的一个新的证明.又,利用非交换单群的极大子群有素数指数的一个结论,本文给出了上述群G可解性的一个新的证明.

As a generalization of Huppert’s theorem,it is shown that if every maximal subgroup of a finite group G which contains the normalizer of some Sylow subgroup has a prime index,the group G is supersolvable.Without applying the solvability of the group G,we give a new proof of its supersolvability.We also give a new proof of the solvability of the above group G by a result of the non-abelian simple group having prime-index maximal subgroups.