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

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/291 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/291 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/291 archive 4031 disk0/00/00/01/10 2008-05-12 14:46:06 2019-01-23 09:51:32 2011-07-19 16:12:58 thesis show 0 Morey Paul Stephen paul_morey@yahoo.co.uk Parker Christopher University of Birmingham The (S_3, A_n)- and (S_3, S_n)-amalgams of characteristic 2 and critical distance 3 unpub QA 30sch_mats Algebra, Group Theory, Amalgams, Amalgam Method 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on the reason why so few of these amalgams are known to exist. 2003-12 graduation 2310869 eng author unchecked This unpublished thesis/dissertation is copyright of the author and/or third parties.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. public 148 University of Birmingham Mathematics and Statistics d_ph epsrc 2003-12 graduation