On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\). (English) Zbl 0816.20043
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.
Reviewer: J.Huebschmann (Bonn)
MSC:
| 20J05 | Homological methods in group theory |
| 20C07 | Group rings of infinite groups and their modules (group-theoretic aspects) |
| 16E10 | Homological dimension in associative algebras |
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