Saturated fusion systems and finite groups

This thesis is primarily concerned with saturated fusion systems over groups of shape q^r : q where q = pⁿ for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems over a Sylow p-subgroup of SL₃(q) (which has shape q³ : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of p-local finite groups over Sylow p-subgroups of SL₃(q). In the second half of this thesis we shall construct an infinite family of exotic fusion systems over some groups of shape p^r : p. This extends some work of Broto, Levi and Oliver, who studied the case when r = 3 in [12].

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

• Clelland, Murray Robinson

• QA Mathematics

Repository record dc:identifier.uri

http://etheses.bham.ac.uk//id/eprint/70/2/Decl_IS_Clelland07PhD.jpg

OAI identifier oai:identifier

oai:etheses.bham.ac.uk:70