p-Groups are not determined by their integral cohomology groups
Algebraic Topology
2007-12-03 v1
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).
Cite
@article{arxiv.0711.4838,
title = {p-Groups are not determined by their integral cohomology groups},
author = {Ian J. Leary},
journal= {arXiv preprint arXiv:0711.4838},
year = {2007}
}