Finite groups in which certain subgroups are Semipermutably embedded

Other Title(s)

الزمر المنتهية ذوات الزمر الجزئية شبه إبدالية الدمج

Dissertant

al-Qadiri, Muwaffaq Umar

Thesis advisor

al-Sharu, Khalid

Comitee Members

al-Ashhab, Salim Shafiq
Sulayman, Ibrahim
Handam, Ali

University

Al albayt University

Faculty

Faculty of Sciences

Department

Department of Mathematics

University Country

Jordan

Degree

Master

Degree Date

2011

English Abstract

A subgroup U of a finite group G is said to be semipermeable in G if U permute with every subgroup V of G such that gcd (| /|, |j / |) = l-For a given prime number p a subgroup U is called p- semipermutably embedded in G if a Sylow p- subgroup of U is a Sylow p - subgroup of some semipermeable subgroup of G.

A subgroup U that is p-semipermutably embedded for every prime p is called semipermutably embedded.

The aim of this thesis is to study this embedding property.

In particular we prove that for some universe of finite solvable groups the class of those groups in which semipermutability is transitive among subgroups coincides with the class of those groups in which p-subgroups are semipermutably embedded in the original group.

Main Subjects

Mathematics

Topics

• Group theory

No. of Pages

56

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-321182