摘要
本文证明了如下的定理：对于有限群Ｇ，下二命题等价：（１）ｐ∈π（Ｇ），Ｇ的Ｓｙｌｏｗｐ－子群及其极大子群皆ｐ－拟正规或自正规；（２）Ｇ为下二型群之一：Ⅰ．幂零群；Ⅱ．Ｇ＝ＱＨ，其中Ｈ是Ｇ的幂零的正规ｑ－补，Ｑ＝〈ｘ〉Ｓｙｌｑ（Ｇ），〈ｘｑ〉＝Ｏｑ（Ｇ）＝Ｚ（Ｇ），ｘ按共轭作用诱导出Ｈ的一个无不动点的自同构．由此定理，得到了每个子群皆Ｓ－拟正规或自正规的有限群的分类定理。
This paper proves the following theorem: for a finite group G, the following two statements are equiualent:(1) for each prime divisor p of |G|, every Sylow p subgroup of G and all its maximal subgroups are p quasi normal or self normal in G; (2) G is one of the following two classes of groups:Ⅰ nilpotent groups; Ⅱ G=QH, where H is the nilpotent normal q complement of G,Q=〈x〉∈Syl q(G),〈x q〉=O q(G)=Z(G) and x induces a fixed proint free automorphism of order q on H by conjugating.From this theorem, the classification theorem of the class of finite groups with only S quasi normal or self normal subgroups is obtained. The main theorems in Frathahi’s(1974) and Zhang’s(1975) papers are the consequences of the present results.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
1997年第3期23-27,共5页
Journal of Sichuan Normal University（Natural Science）
关键词
p-拟正规子群
自正规子群
不动点
自同构
quasi normal subgroup, S quasi normal subgroup, Self normal subgroup, Fixed point free (power) automorphism
