Two Essays on Group Theory

Preface

1. Characterisations of Finite Supersoluble Groups

Introduction

Supersolubility

Supersoluble Series

Sylow Towers and a Theorem of Philip Hall

Some Characterisation Theorems

Further Results

1. Other Finiteness Conditions
2. Images
3. Hypercyclic Groups
4. More on clt Groups
5. Generalised Central Series
6. Finitary Permutation Groups

Abstract

Definitions and Constructions

1. Introduction
2. Generalised Wreath Products
3. Alternating Groups

Primitivity and Imprimitivity

1. Primitivity
2. Imprimitivity
3. A Consequence of the Jordan-Wielandt Theorem
4. An Application

The Commutator Subgroup and Soluble Groups

1. The Shifting Property
2. Soluble and Nilpotent Groups

Local Conditions

1. Definition of Local Properties
2. Locally Soluble Groups
3. Locally Nilpotent Groups

Further Results

1. Results of Segal and Wiegold
2. More Results of P. M. Neumann
3. A Result of Wehrfritz
4. Bibliography