Finite index subgroups without unique product in graphical small cancellation groups

Abstract

We construct torsion-free hyperbolic groups without unique product whose subgroups up to some given finite index are themselves non-unique product groups. This is achieved by generalising a construction of Comerford to graphical small cancellation presentations, showing that for every subgroup $H$ of a graphical small cancellation group there exists a free group $F$ such that $H\ast F$ admits a graphical small cancellation presentation.

8 pages, 1 figure

References in corpus (3)

• Rips-Segev torsion-free groups without the unique product property
• Rips construction without unique product
• Groups with graphical C(6) and C(7) small cancellation presentations

Cited by in corpus (2)

• A counterexample to the unit conjecture for group rings
• Rips construction without unique product