On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\)
type: Item
instance of: scholarly article
title: On groups with \(\text{cd}_ \mathbb{Q} G \leq 1\)
zbMATH Open document ID: 0816.20043
DOI: 10.1016/0022-4049(93)90028-R
author: Olympia Talelli
published in: Journal of Pure and Applied Algebra
publication date: 1995-07-18T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16E10
zbMATH DE Number: 427673
zbMATH Keywords: rational cohomological dimension
zbMATH Keywords: invariants
zbMATH Keywords: \(G\)-module
zbMATH Keywords: projective dimension
reviewed by: J. Huebschmann
MaRDI profile type: Publication
cites work: Q3994461
cites work: Accessibility and Groups of Cohomological Dimension One
cites work: On a property of fundamental groups of graphs of finite groups
cites work: Q3341041
cites work: On cohomological periodicity for infinite groups
cites work: On groups with periodic cohomology after 1-step
cites work: Q3987491
description: scientific article; zbMATH DE number 427673