DOI: 10.1112/blms.70140 ISSN: 0024-6093

Residually nilpotent groups of homological dimension 1

Ioannis Emmanouil
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Abstract

If is a prime number, then any free group is residually a finite ‐group and has homological dimension 1. As a partial converse of this assertion, in this paper we show that any finitely generated group of homological dimension 1, which is residually a finite ‐group, is free. More generally, let be a finite set of prime numbers and denote by the class of those nilpotent groups that have only ‐torsion. We show that any finitely generated group of homological dimension 1, which is residually an ‐group, is free.

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