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

Fowler, Rachel Ann Abbott (2007)
Ph.D. thesis, University of Birmingham.

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Abstract

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.

Type of Work:Ph.D. thesis.
Supervisor(s):Parker, Christopher
School/Faculty:Schools (1998 to 2008) > School of Mathematics & Statistics
Department:Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
Library Catalogue:Check for printed version of this thesis
ID Code:113
This unpublished thesis/dissertation is copyright of the author and/or third parties.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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