Leary, Ian J.
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).
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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.
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