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The (S_3, A_n)- and (S_3, S_n)-amalgams of characteristic 2 and critical distance 3

Morey, Paul Stephen (2003)
Ph.D. thesis, University of Birmingham.

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Abstract

In this thesis a new characterisation of the (S_3, A_n)- and (S_3, S_n)-amalgams of characteristic 2 and critical distance 3 is obtained. It is shown that such an amalgam exists only in the exceptional cases when n=3, 5 or 8. Let C denote the class of all finite groups X of even order and such that O^2(X) is the unique minimal normal subgroup of X. It is the secondary purpose of this thesis to begin an investigation into the structure of the (S_3, C)-amalgams of characteristic 2 and critical distance 3. It is hoped that the results obtained may shed some light on the reason why so few of these amalgams are known to exist.

Type of Work:Ph.D. thesis.
Supervisor(s):Parker, Christopher
School/Faculty:Schools (1998 to 2008) > School of Mathematics & Statistics
Department:Mathematics and Statistics
Keywords:Algebra, Group Theory, Amalgams, Amalgam Method
Subjects:QA Mathematics
Institution:University of Birmingham
Library Catalogue:Check for printed version of this thesis
ID Code:110
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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