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Title: Saturated fusion systems and finite groups
Author: Clelland, Murray Robinson
ISNI:       0000 0001 3558 8658
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2007
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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].
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics