Johnson, D. L.. (1968) On the cohomology of finite groups over modular fields. PhD thesis, University of Warwick.

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Abstract

The aim of this thesis is to study the cohomology of a finite group G by means of certain of its modular representations. For such an approach to be possible, it is necessary to restrict our attention to the case where the coefficient module is a vector space over some field K of characteristic p dividing the order of G. When this is done, it is possible, in view of Theorem 1.1, to work entirely within the category of finitely-generated KG-modules. The simplifications in the theory which are thus achieved compensate in some measure for the attendant loss of generality. In fact, we hope to put forward a case that the natural way to study the cohomology of a finite group, at least from an algebraic point of view, is within the above-mentioned category. Although much of what follows remains true for representations over p-adic rings, and the loss of generality is not so great in this case, we restrict ourselves to fields of characteristic p for the sake of simplicity. In fact, in view of Remark 2.13, no further loss of generality is sustained by considering only the field of p elements.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Finite groups, Modular representations of groups, Group theory, Homology theory, Algebraic topology
Official Date:	1968
Dates:	Date Event 1968 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Publication Status:	Unpublished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:	85 leaves
Language:	eng

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