有限群超可解的两个充要条件

Two Sufficient and Essential Conditions for Supersolvability of Finite Groups

本文主要讨论了部分极小子群和部分极大子群Ｓ－半正规的有限群，得到有限群超可解的两个充要条件。

In this paper the auther discusses finite groups which some minimal subgroups and maximal subgroups are S-seminormality in G. The main result is as follows:Theorem Ⅰ Let G be a finite group and N. a normal subgroup of G suth that G/N is supersolvable and every minimal subgroups pf N is S-seminormal in G .Then G is supersolvable if and only if G is D2q-free. Theorem Ⅱ Let G be a finite group and N .a normal subgroup of G such that G/N is Supersolvable and every maximal subgroup of sylow subgroups of N is S-seminormal in G.Then G is Supersolvable if and only if here is P-Sylon subgroup Gp of G, Such that G'p is normal subgroup of G for each prime disisor P of G.