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Spherical quadratic equations in free metabelian groups


Authors: Igor Lysenok and Alexander Ushakov
Journal: Proc. Amer. Math. Soc. 144 (2016), 1383-1390
MSC (2010): Primary 20F16; Secondary 20F10, 68W30
DOI: https://doi.org/10.1090/proc/12662
Published electronically: December 22, 2015
MathSciNet review: 3451217
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Abstract: We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, $ \mathbf {NP}$-complete.


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Additional Information

Igor Lysenok
Affiliation: Department of Mathematical Logic, Steklov Institute of Mathematics, Gubkina str. 8, 119991 Moscow, Russia – and – Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030
Email: igor.lysenok@gmail.com

Alexander Ushakov
Affiliation: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, New Jersey 07030
Email: aushakov@stevens.edu

DOI: https://doi.org/10.1090/proc/12662
Keywords: Free metabelian group, Diophantine problem, quadratic equation, $\NP$-completeness
Received by editor(s): June 8, 2014
Received by editor(s) in revised form: August 25, 2014
Published electronically: December 22, 2015
Additional Notes: The first author has been partially supported by the Russian Foundation for Basic Research
The second author has been partially supported by NSA Mathematical Sciences Program grant number H98230-14-1-0128
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2015 American Mathematical Society