Equations in nilpotent groups
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- by Moon Duchin, Hao Liang and Michael Shapiro PDF
- Proc. Amer. Math. Soc. 143 (2015), 4723-4731 Request permission
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.References
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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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4723-4731
- MSC (2010): Primary 20F10, 20F18, 20F70
- DOI: https://doi.org/10.1090/proc/12630
- MathSciNet review: 3391031