Blocks with an elementary abelian defect group in characteristic two

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.

Date of Award	31 Dec 2020
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Marianne Johnson (Supervisor) & Charles Eaton (Supervisor)