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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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