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The Influence of Generalized Supplemented Subgroups on the Structure of Finite Groups

Author: DongShuQin
Tutor: WeiHuaQuan
School: Guangxi Normal University
Course: Basic mathematics
Keywords: finite group maximal subgroup minimal subgroup supersolvable p-nilpotent solvable
CLC: O152.1
Type: Master's thesis
Year: 2010
Downloads: 13
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Abstract


In this paper, we investigate the properties of generalized supplemented subgroups:weakly s-supplemented subgroup, ss-supplemented subgroup, c*-normal subgroup, X-semipermutable subgroups in finite groups, with which we characterize the structure of some subgroups by the maximal subgroups and minimal subgroups of Sylow subgroups, and obtain some meaningful results. The body of the paper is divided into three chapters:Chapter 1 concerns with the influence of weakly s-supplemented subgroups and ss-supplemen-ted subgroups on the strucure of finite groups. First, we get some sufficient conditions on p-nilpotency and solvability of finite groups with minimal weakly s-supplemented subgroups. Second, as a unified generalization of the concept of weakly s-supplemented subgroup, we intro-duce a new concept called ss-supplemented subgroup and characterize the solvability of a finite group with ss-supplemented subgroups of Sylow subgroups and maximal subgroups of its.In chapter 2, we study the influence of the local subgroups by considering two characteristics of subgroups, namely, weakly s-supplemented and c*-normal subgroup, on the strucure of finite groups. Thus, we obtain the p-nilpotency and supersolvability of finite groups and generalize some recent related results.Chapter 3 is mainly to study the influence of X-semipermutable subgroups on the strucure of finite groups. With "Md(P)", we decrease the number of X-semipermutable subgroups and get some sufficient conditions on p-nilpotency, (p-)supersolvability of finite groups.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Finite group theory
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