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

Fowler, Rachel Ann Abbott (2007). A 3-local characterization of the group of the Thompson sporadic simple group. University of Birmingham. Ph.D.

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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:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

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