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arXiv · 0711.4838

p-Groups are not determined by their integral cohomology groups

Ian J. Leary
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Abstract

For each prime p, we exhibit pairs of p-groups all of whose integral cohomology groups are isomorphic. The method used involves very little calculation. The groups are exhibited as kernels of homomorphisms from a compact Lie group G to U(1), and the main result is that kernels of `similar' elements of Hom(G,U(1)) have isomorphic integral cohomology groups. The 2-groups constructed in this version have been corrected (there was a mistake in the presentations given in the published paper).

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Ian J. Leary. 2007-11-29. p-Groups are not determined by their integral cohomology groups. https://arxiv.org/abs/0711.4838

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