Spherical quadratic equations in free metabelian groups
Igor Lysenok, Alexander Ushakov
TL;DR
This paper proves that solving spherical quadratic equations in free metabelian groups is both decidable and NP-complete, advancing understanding of computational problems in algebraic group theory.
Contribution
It establishes the NP-completeness of the Diophantine problem for spherical quadratic equations in free metabelian groups, a novel complexity result.
Findings
The Diophantine problem for these equations is solvable.
The problem is NP-complete.
Provides complexity classification for a class of algebraic equations.
Abstract
We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, NP-complete
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