3-groups are not determined by their integral cohomology rings
3-groups are not determined by their integral cohomology rings
There is one compact 1-dimensional Lie group with 27 components and nilpotence class three. We give a presentation for the integral cohomology ring of this group. We show that finite groups of order 81 can be distinguished by their first few integral cohomology groups, and we exhibit a pair of groups of order 243 that have isomorphic integral cohomology rings.
61-79
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
25 August 1995
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Leary, Ian J.
(1995)
3-groups are not determined by their integral cohomology rings.
Journal of Pure and Applied Algebra, 103 (1), .
(doi:10.1016/0022-4049(95)00092-B).
Abstract
There is one compact 1-dimensional Lie group with 27 components and nilpotence class three. We give a presentation for the integral cohomology ring of this group. We show that finite groups of order 81 can be distinguished by their first few integral cohomology groups, and we exhibit a pair of groups of order 243 that have isomorphic integral cohomology rings.
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Published date: 25 August 1995
Organisations:
Pure Mathematics
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Local EPrints ID: 199323
URI: http://eprints.soton.ac.uk/id/eprint/199323
PURE UUID: 5b513ed3-890c-428c-95c1-83c44e0aa0d0
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Date deposited: 18 Oct 2011 10:34
Last modified: 15 Mar 2024 03:36
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