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On the cohomology of finite groups over modular fields

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

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Official URL: http://webcat.warwick.ac.uk/record=b1722697~S1

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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:
DateEvent
1968Submitted
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Publication Status: Unpublished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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