On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\) (Q686043)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\) |
scientific article; zbMATH DE number 427673
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\) |
scientific article; zbMATH DE number 427673 |
Statements
On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\) (English)
0 references
18 July 1995
0 references
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.
0 references
rational cohomological dimension
0 references
invariants
0 references
\(G\)-module
0 references
projective dimension
0 references
