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The subring of group cohomology constructed by permutation representations

The subring of group cohomology constructed by permutation representations
The subring of group cohomology constructed by permutation representations
Every homomorphism from a finite group G to a symmetric group S gives rise to a homomorphism from the mod-p cohomology of S to that of G. We describe the prime ideal spectrum of the subring of the cohomology of G generated by all such representations. This subring turns out to be amenable to the techniques introduced by two of us in 15. Much of the paper consists of a comparison of the prime ideal spectra for three distinct rings in the case when G is the general linear group GL(n,p) over the field of p elements. These are the whole mod-p cohomology ring, the subring corresponding to all permutation representations (as described above), and the subring corresponding to the permutation actions on partial flags. For n large and even, we show that no two of these rings are F-isomorphic.
241-253
Green, David J.
631334e7-9a9a-427f-badb-d274f426ca64
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Schuster, Björn
8a0644ba-2472-4722-98db-f4caee5fd36c
Green, David J.
631334e7-9a9a-427f-badb-d274f426ca64
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Schuster, Björn
8a0644ba-2472-4722-98db-f4caee5fd36c

Green, David J., Leary, Ian J. and Schuster, Björn (2002) The subring of group cohomology constructed by permutation representations. Proceedings of the Edinburgh Mathematical Society, 45 (1), 241-253.

Record type: Article

Abstract

Every homomorphism from a finite group G to a symmetric group S gives rise to a homomorphism from the mod-p cohomology of S to that of G. We describe the prime ideal spectrum of the subring of the cohomology of G generated by all such representations. This subring turns out to be amenable to the techniques introduced by two of us in 15. Much of the paper consists of a comparison of the prime ideal spectra for three distinct rings in the case when G is the general linear group GL(n,p) over the field of p elements. These are the whole mod-p cohomology ring, the subring corresponding to all permutation representations (as described above), and the subring corresponding to the permutation actions on partial flags. For n large and even, we show that no two of these rings are F-isomorphic.

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Published date: 2002

Identifiers

Local EPrints ID: 29835
URI: http://eprints.soton.ac.uk/id/eprint/29835
PURE UUID: 98254089-2b12-4701-bfd7-ad9ab935b325
ORCID for Ian J. Leary: ORCID iD orcid.org/0000-0001-8300-4979

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Date deposited: 12 May 2006
Last modified: 08 Jan 2022 03:12

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Contributors

Author: David J. Green
Author: Ian J. Leary ORCID iD
Author: Björn Schuster

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