Characterizations of finite supersoluble groups

Supersolubility and some characterizations of finite supersoluble groups

In 1997, I graduated with a four-year undergraduate MSci masters degree. I was one of four who did the extended programme at Queen Mary and Westfield College. The first three years were identical to a BSc and the fourth year consisted of six MSc level courses along with a project that had to be completed simultaneously. The MSc has a project that is usually completed over the summer or in a subsequent year.

The project is available for download on this page. I worked under the supervision of Prof B.A.F. Wehrfritz. I’m not sure who my examiners were but after attending a conference I discovered that Prof Alan Camina was one of them.

Although I submitted the project in 1997, I revised it during the first year of my PhD to typeset it in LateX and make some minor corrections.

Abstract

This project gathers together results regarding supersoluble groups. A supersoluble group is a group which can be broken down into cyclic groups by means of a normal series.

The class of supersoluble groups sits between the classes of finitely generated nilpotent groups and polycyclic groups. Supersoluble groups are, in some sense, more like nilpotent groups than polycyclic groups. Finite supersoluble groups have some very nice characterisations in terms of their subgroup structure and we will investigate these in this document.

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