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Title: Centralisers and amalgams of saturated fusion systems
Author: Semeraro, Jason P. G.
ISNI:       0000 0004 2747 6164
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2013
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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.
Supervisor: Collins, Michael J.; Craven, David A. Sponsor: EPSRC
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Group theory and generalizations (mathematics) ; finite group theory ; saturated fusion systems