Equations in nilpotent groups
Group Theory
2014-01-14 v1
Abstract
We show that there exists an algorithm to decide any single equation in the Heisenberg group in finite time. The method works for all two-step nilpotent groups with rank-one commutator, which includes the higher Heisenberg groups. We also prove that the decision problem for systems of equations is unsolvable in all non-abelian free nilpotent groups.
Cite
@article{arxiv.1401.2471,
title = {Equations in nilpotent groups},
author = {Moon Duchin and Hao Liang and Michael Shapiro},
journal= {arXiv preprint arXiv:1401.2471},
year = {2014}
}