3-groups are not determined by their integral cohomology rings Original Research Article

There is exactly one compact 1-dimensional Lie group having 27 components and nilpotence class three. We give a presentation for the integral cohomology ring of (the classifying space of) this group. We show that the groups of order 34 can be distinguished by their first few integral cohomology groups, and exhibit a pair of groups of order 35 having isomorphic integral cohomology rings.