In this thesis, we mainly address two contrasting topics in the area of saturated fusion systems. The first concerns the notion of a centraliser of a subsystem E of a fusion system F, and we give new proofs of the existence of such an object in the case where E is normal in F. The second concerns the development of the theory of `trees of fusion systems', an analogue for fusion systems of Bass-Serre theory for finite groups. A major theorem finds conditions on a tree of fusion systems for there to exist a saturated completion, and this is applied to construct and classify certain fusion systems over p-groups with an abelian subgroup of index p. Results which do not fall into either of the above categories include a new proof of Thompson's normal p-complement Theorem for saturated fusion systems and characterisations of certain quotients of fusion systems which possess a normal subgroup.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:581408 |
| Date | January 2013 |
| Creators | Semeraro, Jason P. G. |
| Contributors | Collins, Michael J.; Craven, David A. |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:43d7d6d0-363b-4bc7-b17f-5713cc586737 |
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