含指数为素数幂的超可解子群的有限群

FINITE GROUPS WITH SUPERSOLVABLE SUBGROUPS OF PRIME POWER INDEX

本文讨论含指数为素数幂的超可解子群的有限群的结构.首先得到具有这种性质的非Abel有限单群的完全分类定理.其次给出了这类群是可解群和超可解群的若干充分条件.

In this paper,we discuss the structure of finite groups with supersolvable subgroups of prime power index.First,we obtain the complete classification theorem of non-abelian finite simple groups with this property:G is a nonabelian simple group containing supersolvable maximal subgroups with prime power index if and only if G =PSL 2 (q),where q>3,a Mersenne prime.Next,we provide some sufficient conditions of finite solvable groups and finite solvable groups and finite supersolvable groups.