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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. Parker, Christopher Schools (1998 to 2008) > School of Mathematics & Statistics Mathematics QA Mathematics University of Birmingham Check for printed version of this thesis 113
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