One-relator groups with torsion are coherent

We show that any one-relator group $G = F / {\langle \negthinspace \langle} w {\rangle \negthinspace \rangle}$ with torsion is coherent — i.e., that every finitely generated subgroup of $G$ is finitely presented — answering a 1974 question of Baumslag in this case.

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The authors were supported by EPSRC Standard Grant EP/L026481/1.

Received 30 May 2018

Accepted 30 June 2020

Published 12 January 2021