\(3\)-groups are not determined by their integral cohomology rings (Q1901022)

The author proves that groups of order \(3^4\) can be distinguished by their first few integral cohomology groups and produces two non-isomorphic groups of order \(3^5\) having isomorphic integral cohomology groups. The latter examples are found as normal subgroups of a single compact 1-dimensional Lie group with connected quotients, and the method involves finding the cohomology of this Lie group.