p-Groups are not determined by their integral cohomology groups

Details p-Groups are not determined by their integral cohomology groups p-Groups are not determined by their integral cohomology groups

2007-11-29

arxiv.org/abs/0711.4838v1

Bull. London Math. Soc. 27 (1995) 585--589

Mathematics

Algebraic Topology

Scientific paper

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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