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Saturated fusion systems and finite groups

Clelland, Murray Robinson (2007)
Ph.D. thesis, University of Birmingham.

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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:Ph.D. thesis.
Supervisor(s):Parker, Christopher
School/Faculty:Schools (1998 to 2008) > School of Mathematics & Statistics
Department:Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
Library Catalogue:Check for printed version of this thesis
ID Code:70
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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