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5.8 (1976)

Solved

Let $G$ be a torsion-free soluble group of finite cohomological dimension $\text{cd}\,G$. If $hG$ denotes the Hirsch number of $G$, then it is known that $hG \leqslant \text{cd}\,G \leqslant hG+ 1$. Find a purely group-theoretic criterion for $hG = \text{cd}\,G$.

Contributor: K. W. Gruenberg

Progress

This has been found (P. H. Kropholler, J. Pure Appl. Algebra, 43 (1986), 281–287).

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