3-groups are not determined by their integral cohomology rings

Leary, Ian J. (1995) 3-groups are not determined by their integral cohomology rings. Journal of Pure and Applied Algebra, 103, (1), 61-79. (doi:10.1016/0022-4049(95)00092-B).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/0022-4049(95)00092-B
ISSNs: 0022-4049 (print)
Subjects: Q Science > QA Mathematics
Divisions : Faculty of Social and Human Sciences > Mathematical Sciences > Pure Mathematics
ePrint ID: 199323
Accepted Date and Publication Date:
25 August 1995Published
Date Deposited: 18 Oct 2011 10:34
Last Modified: 31 Mar 2016 13:45
URI: http://eprints.soton.ac.uk/id/eprint/199323

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