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Weakly S-Semipermutable Subgoups and SS-Supplement Subgroups

Author: LiJie
Tutor: QianFangSheng
School: Harbin Normal University
Course: Basic mathematics
Keywords: the s- Semipermutable subgroup The weak s - Semipermutable - subgroup ss- Supplemented Subgroups p - nilpotent groups Supersolvable groups
CLC: O152.1
Type: Master's thesis
Year: 2011
Downloads: 25
Quote: 0
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Abstract


The structure of the group and is closely related to the nature of some subgroups , group of a different structure can be obtained by the study of the nature of the different sub- groups . Subgroup H of the finite group G is referred to as the s- semipermutable , if for any prime number p | | G |, as long as ( p , | H | ) = 1, there is pH HP, where P ∈ Sylp (G) subgroup H of a finite group G the weak s - semipermutable - subgroup T ≤ G G = HT and H ∩ T ≤ HSSG which HSSG contains H in G the s- semipermutable sub group H is a finite group G ss- complemented subgroup T ≤ G , if there , making the HT is s- permutable subgroups in G and H ∩ T ≤ HSG HSG is contained in H of G s- permutable subgroups paper combines some special subgroups of finite groups (eg , Sylow subgroups cyclic subgroup of maximal subgroups of Sylow subgroup ), weak s- half replacement and ss- complementary to study finite group of p - nilpotency super solvability sufficient condition to promote some results of a number of documents . according to the content of this article is divided into the following three parts : The first part introduces the research background of the issues involved , and summarizes the main results of this paper . listed in the second part of this article is closely related to some of the basic concept and lemma . third part mainly weak s- semi- permutable subgroups and the ss- complemented subgroups nature get the sufficient condition for p- nilpotency of finite groups and ultra- solvability .

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