Odd characterizations of almost simple groups - 3-local and character theoretic methods

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/1255 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/1255 http://eprints.org/relation/issmallThumbnailVersionOf http://etheses.bham.ac.uk/id/document/1255 archive 4031 disk0/00/00/05/20 2010-02-09 10:16:57 2019-01-23 09:52:19 2011-07-19 16:18:51 thesis show 0 Astill Sarah Parker Christopher University of Birmingham Odd characterizations of almost simple groups - 3-local and character theoretic methods unpub QA 10col_ephy Mathematics, group theory, classification of finite simple groups In this PhD thesis we discuss methods of recognizing finite groups by the structure of normalizers of certain 3-subgroups. We explain a method for characterizing groups using character theoretic and block theoretic methods and we use these methods to characterize Alt(9). Furthermore, we describe a particular hypothesis related to the 3-local structure of finite groups of local characteristic 3 and characterize two almost simple proper extensions of \(\Omega\)\(_8\) (2) as examples of the local approach to group recognition. We also give a 3-local characterization of the sporadic simple group HN using local methods whilst applying a character theoretic result. 2010-07 graduation eng This unpublished thesis/dissertation is copyright of the author and/or third parties.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 189 University of Birmingham School of Mathematics d_ph na 2010-07 graduation