On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\)
A group \(G\) is said to have property \({\mathcal P}_ 1\) if there is a \(G\)- module \(T\) which is free as an abelian group, has projective dimension at most 1 over \(G\), and has non-trivial \(G\)-invariants \(T^ G\). It is proved that a group has property \({\mathcal P}_ 1\) if and only if over the rationals it has cohomological dimension at most 1.
scientific article; zbMATH DE number 427673