A 3-local characterization of the group of the Thompson sporadic simple group

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/298 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/298 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/298 archive 4031 disk0/00/00/01/13 2008-05-14 09:22:12 2019-01-23 09:51:33 2011-07-19 16:13:00 thesis show 0 Fowler Rachel Ann Abbott rachel.ann.fowler@googlemail.com Parker Christopher University of Birmingham A 3-local characterization of the group of the Thompson sporadic simple group unpub QA 30sch_mats In this thesis we characterize the Thompson sporadic simple group by its 3-local structure. We study a faithful completion, \(G\), of an amalgam of type F\(_3\) with the property that \(N_G(Z(L_\beta)) = G_\beta\). We first assume no additional 3-local structure and use a \(\kappa\)-proper hypothesis to establish that the completion \(G\) with this property contains a subgroup \(Y\) of order 3 such that \(N_G(Y)\cong (3 \times\) G\(_2\)(3)) : 2. Secondly, we assume that \(G\) contains such a subgroup \(Y\) with \(N_G(Y)\cong (3 \times\) G\(_2\)(3)) : 2 and show that for an involution \(t \in G, C_G(t)\) has shape 2\(^{1+8}_+\).Alt(9). We then invoke a theorem of Parrott to show that \(G \cong \) Th. 2007-07 graduation 2626013 eng other unchecked From Supervisor's web page, with author's permission This unpublished thesis/dissertation is copyright of the author and/or third parties.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 134 University of Birmingham School of Mathematics d_ph epsrc 2007-07 graduation