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Title: Complementation in finite groups
Author: MacLean, David Murdoch
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1972
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This thesis is a study of the restrictions which are imposed on the structure of a finite group by some conditions on its lattice of subgroups. The conditions considered fall into two categories: either (1) the demand is made that certain of the subgroups of the group should have complements, or (2) it is specified that all subgroups should have supplements of a particular kind. There are three chapters. Chapter 1 develops some techniques and results about complements and pronormality which are used later, mainly in Chapter 2. A problem from category (1) above is the subject of Chapter 2, which is an investigation of finite groups with the property that all the pro normal subgroups have complements. Necessary and sufficient conditions are given for a soluble group of derived length at most 3 to have that property. Chapter 3 is concerned with category (2); the basic theme is that of a finite group G in which each subgroup H has a supplement S such that H n S belongs to some prescribed class X.
Supervisor: Not available Sponsor: Carnegie Trust for the Universities of Scotland
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics