Equations in virtually class 2 nilpotent groups

Abstract

We give an algorithm that decides whether a single equation in a group that is virtually a class $2$ nilpotent group with a virtually cyclic commutator subgroup, such as the Heisenberg group, admits a solution. This generalises the work of Duchin, Liang and Shapiro to finite extensions.

Keywords

• mathematics - group theory
• 20f10, 20f18, 03b25