Use this URL to cite or link to this record in EThOS:
Title: A 3-local characterization of the group of the Thompson sporadic simple group
Author: Fowler, Rachel Ann Abbott
ISNI:       0000 0001 3479 090X
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2007
Availability of Full Text:
Access from EThOS:
Access from Institution:
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:  DOI: Not available
Keywords: QA Mathematics