Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.489758
Title: A 3-local characterization of the group of the Thompson sporadic simple group
Author: Fowler, Rachel Ann Abbott
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2007
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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.
Supervisor: Not available Sponsor: EPSRC (Engineering and Physical Sciences Research Council)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.489758  DOI: Not available
Keywords: QA Mathematics
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