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].
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:446348 |
| Date | January 2007 |
| Creators | Clelland, Murray Robinson |
| Publisher | University of Birmingham |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://etheses.bham.ac.uk//id/eprint/70/ |
Page generated in 0.0023 seconds