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Centralisers and amalgams of saturated fusion systems

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.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:581408
Date January 2013
CreatorsSemeraro, Jason P. G.
ContributorsCollins, Michael J.; Craven, David A.
PublisherUniversity of Oxford
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttp://ora.ox.ac.uk/objects/uuid:43d7d6d0-363b-4bc7-b17f-5713cc586737

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