# Saturated fusion systems and finite groups

Clelland, Murray Robinson (2007). Saturated fusion systems and finite groups. University of Birmingham. Ph.D.

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## Abstract

This thesis is primarily concerned with saturated fusion systems over groups of shape q$$^r$$ : q where q = p$$^n$$ 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 SL$$_3$$(q) (which has shape q$$^3$$ : 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 SL$$_3$$(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].

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Supervisor(s):
Supervisor(s)EmailORCID
Parker, ChristopherUNSPECIFIEDUNSPECIFIED
Licence:
College/Faculty: Schools (1998 to 2008) > School of Mathematics & Statistics
School or Department: School of Mathematics
Funders: None/not applicable
Subjects: Q Science > QA Mathematics
URI: http://etheses.bham.ac.uk/id/eprint/70

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