Mathematical Research Letters

Volume 27 (2020)

Number 5

One-relator groups with torsion are coherent

Pages: 1499 – 1511



Larsen Louder (Department of Mathematics, University College London, United Kingdom)

Henry Wilton (DPMMS, Cambridge University, Cambridge, United Kingdom)


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.

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

Received 30 May 2018

Accepted 30 June 2020

Published 12 January 2021