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Equations in nilpotent groups


Authors: Moon Duchin, Hao Liang and Michael Shapiro
Journal: Proc. Amer. Math. Soc. 143 (2015), 4723-4731
MSC (2010): Primary 20F10, 20F18, 20F70
DOI: https://doi.org/10.1090/proc/12630
Published electronically: April 10, 2015
MathSciNet review: 3391031
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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.


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Additional Information

Moon Duchin
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: Moon.Duchin@tufts.edu

Hao Liang
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: Hao.Liang@tufts.edu

Michael Shapiro
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: Michael.Shapiro@tufts.edu

DOI: https://doi.org/10.1090/proc/12630
Received by editor(s): March 6, 2014
Received by editor(s) in revised form: August 29, 2014
Published electronically: April 10, 2015
Additional Notes: The first author was partially supported by NSF grants DMS-1207106 and DMS-1255442.
The third author wishes to acknowledge support from NIH grant K25 AI079404-05.
Communicated by: Kevin Whyte
Article copyright: © Copyright 2015 American Mathematical Society