Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.816362
Title: Blocks with an elementary abelian defect group in characteristic two
Author: Ardito, Cesare Giulio
ISNI:       0000 0004 9354 2780
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2020
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Abstract:
This thesis concerns the problem of classifying blocks with an elementary abelian defect group, and in particular blocks with an elementary abelian defect group of order 32. In Chapter 1 we establish the notation and introduce the key objects and arguments on which modular representation theory and block theory are built. In Chapter 2 we introduce (G, B)-local systems and crossed products, which we use to investigate block covering relations, and we describe a general method that can be used to classify blocks once a specific list of prerequisites has been achieved. In Chapter 3 we employ this method to classify blocks with an elementary abelian defect group of order 32. Due to the lack of all necessary prerequisites, we employ alternative, more ad-hoc techniques to obtain the result. These techniques, while less general, still have good potential to be useful in many more other cases. In Chapter 4 we examine the case of blocks with an elementary abelian defect group of order 64, and we classify all principal blocks with such defect group.
Supervisor: Johnson, Marianne ; Eaton, Charles Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.816362  DOI: Not available
Keywords: Block theory ; Donovan's conjecture ; Finite groups ; Morita equivalence ; Modular representation theory
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