McLean, Joseph Francis
(1985)
Finite Group Theory: Odd Primes and CCSubgroups.
MSc(R) thesis, University of Glasgow.
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Abstract
The majority of this thesis comprises a survey of existing knowledge. Let G be a finite group and suppose that M is a subgroup of G such that (i)1<M<G, and (ii)for all x∈M#,CG(x)≤M. Such a subgroup M is called a CCsubgroup the concept to which this thesis is predominantly devoted. Following a brief introduction. Chapter 11 consists of a survey of the known results on the odd prime structure of finite groups. This survey is split into three sections as follows. The first gives an account of the development of a unified theory for characterising groups with CCsubgroups of order divisible by three. Section II introduces the twin ideas of closure and homogeneity, concluding with a theorem which has Important applications later in Chapter V. Section ill consists of a straightforward listing of the remaining odd prime structure results. Chapter III is the theoretical base of the thesis, contributing all the major results which are required before proceeding. Section II of this chapter is itself an integral part of the survey, being a systematic exposition of basic CCsubgroup theory. Chapter IV is a discussion on the various techniques and proofs Involved In Chapter II, giving a readable yet rigorous explanation of the theory. Chapter V highlights more recent, and more general, results involving CCsubgroups, giving detailed proofs, and sets the scene for the final chapter. Chapter VI consists of two sections. Section I is given over entirely to the statement and proof of a single theorem which completely classifies groups containing CCsubgroups, a simple corollary of which Initiates Section II, an outline of the search for CCsubgroups of the finite simple groups. This section, and the thesis, ends with four tables that give as complete a list as possible of the Information currently available on the CCsubgroups of the simple groups.
Item Type: 
Thesis
(MSc(R))

Qualification Level: 
Masters 
Additional Information: 
Adviser: Neil K Dickson 
Keywords: 
Theoretical mathematics 
Date of Award: 
1985 
Depositing User: 
Enlighten Team

Unique ID: 
glathesis:198576428 
Copyright: 
Copyright of this thesis is held by the author. 
Date Deposited: 
19 Nov 2019 14:31 
Last Modified: 
19 Nov 2019 14:31 
URI: 
http://theses.gla.ac.uk/id/eprint/76428 
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