Peacock, Richard Martin (1974) Blocks with a cyclic defect group. PhD thesis, University of Warwick.

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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.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Blocks (Group theory), Finite groups
Official Date:	1974
Dates:	Date Event 1974 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Green, J. A. (James Alexander)
Sponsors:	Science Research Council (Great Britain)
Extent:	87 leaves
Language:	eng

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