Document Details

Document Type : Thesis 
Document Title :
THE IMPACT OF CERTAIN KINDS OF SUBGROUPS WITH SPECIAL PROPERIES ON THE STRUCTURE OF FINITE GROUPS
تأثير أنواع معينة من الزمر الجزئية ذات خصائص مميزة على بنية الزمر المنتهية
 
Subject : Faculty of Sciences 
Document Language : Arabic 
Abstract : Let H and K be subgroups of a finite group G. The subgroups H and K are said to be permutable if HK=KH, in other words, HK is a subgroup of G. We study different aspects about the structure of finite groups by introducing some new ideas involving permutability combined with other notions from group theory. Namely, we present the concept of complete Hall 𝔉-sets and Z-permutability as well as the concept of SSH-subgroups. Let G be a group. In the concept of complete Hall 𝔉-set and Z-permutability, we define Z to be a set that is associated with the group G and 𝔉 to be some suitable class of groups. More precisely, all the members of the set Z are Hall subgroups of G which are contained in 𝔉 with the additional property that for each prime p ∈π(G), p divides the order of only one member of Z. We will say that a subgroup H of G is Z-permutable in G if H permutes with every member of Z. Let H be a subgroup of a group G. We say that H is s-permutable in G if H permutes with every Sylow subgroup of G. Also, we say that H is an H-subgroup in G if H^g∩N_G (H)⩽H, for all g∈G. The notion of SSH-subgroups provides a connection between the concepts of s-permutability and H-subgroups. We will examine the structure of a finite group G under the assumption that some subgroups of prime index of particular subgroups of G are Z-permutable in G. In addition, we will examine the factor group H/H_G when H is a subnormal Z-permutable subgroup of G. These investigations will be done by considering complete Hall 𝔉-sets for various classes of groups. On the other hand, we will use the concept of SSH-subgroups to analyze the structure of G under the assumption that certain subgroups of prime power orders of G are SSH-subgroups in G. 
Supervisor : Prof. Syed Khalid Nauman 
Thesis Type : Doctorate Thesis 
Publishing Year : 1439 AH
2018 AD 
Added Date : Monday, July 30, 2018 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
طالب محسن الجفريAl-Gafri, Taleb MohsenResearcherDoctorate 

Files

File NameTypeDescription
 43645.pdf pdf 

Back To Researches Page