MacLean, David Murdoch (1972) Complementation in finite groups. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Finite groups, Group theory
Official Date:	June 1972
Dates:	Date Event June 1972 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Stonehewer, Stewart E. (Stewart Edward),‏ 1935-
Sponsors:	Carnegie Trust for the Universities of Scotland
Extent:	133 leaves
Language:	eng

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