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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
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) | ||||
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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: |
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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Publication Status: | Unpublished | ||||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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