Leary, Ian J. (1995) p-Groups are not determined by their integral cohomology groups. Bulletin of the London Mathematical Society, 27 (6), 585-589. (doi:10.1112/blms/27.6.585).
Abstract
For each prime p we exhibit non-isomorphic p-groups that have isomorphic integral cohomology groups. We give an indirect proof rather than a computation. The examples for p=2 in the original paper were flawed; an erratum repaired this.
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