Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.595045
Title: Blocks with a cyclic defect group
Author: Peacock, Richard Martin
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1974
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Abstract:
This thesis is concerned with the block theory of a finite group over an algebraically closed field of prime characteristic. We study the indecomposable modules in such a block Ḇ.with a cyclic defect group, and then the results that we get are applied to the principal p-blocks of the symmetric group Sp' the alternating group ~ and the five Mathieu groups, Ap being an odd prime. There are three parts to this thesis, each one dealing with the following topics. Part A is concerned with finding the full submodule lattice of each one of the projective indecomposable modules in Ḇ. These lattices turn out to have simple diamond shapes, and depend upon parameters r(i),s(i). In part B we generalise the methods used in the previous part to get a good description of a full set of non-projective indecomposables in Ḇ.(though we do not manage to get their full submodule lattices). Finally in part C we show how to use ordinary character theory, and in particular the Brauer tree, to work out these positive integers r(i),s(i) and then we apply such methods to work out the lattices of those examples listed above.
Supervisor: Not available Sponsor: Science Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.595045  DOI: Not available
Keywords: QA Mathematics
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