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

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 F₃ 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 G₂(3)) : 2. Secondly, we assume that \(G\) contains such a subgroup \(Y\) with N_G(Y)\cong (3 \times G₂(3)) : 2 and show that for an involution t \in G, C_G(t) has shape 2¹⁺⁸₊.Alt(9). We then invoke a theorem of Parrott to show that \(G \cong \) Th.

Name dc:type.qualificationname

d_ph

Level dc:type.qualificationlevel

d_ph

Grantor dc:publisher.institution

University of Birmingham

Year dc:date.issued

2007

Author dc:creator

• Fowler, Rachel Ann Abbott

• QA Mathematics