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.
Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:489758 |
Date | January 2007 |
Creators | Fowler, Rachel Ann Abbott |
Publisher | University of Birmingham |
Source Sets | Ethos UK |
Detected Language | English |
Type | Electronic Thesis or Dissertation |
Source | http://etheses.bham.ac.uk//id/eprint/113/ |
Page generated in 0.0014 seconds