Spherical quadratic equations in free metabelian groups

Igor Lyseno; Alexander Ushakov

doi:10.1090/proc/12662

Spherical quadratic equations in free metabelian groups

Igor Lyseno
, Alexander Ushakov

Department of Mathematical Sciences

RAS - Steklov Mathematical Institute

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, NP-complete.

Original language	English
Pages (from-to)	1383-1390
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	4
DOIs	https://doi.org/10.1090/proc/12662
State	Published - Apr 2016

Keywords

Diophantine problem
Free metabelian group
NP-completeness
Quadratic equation

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10.1090/proc/12662

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title = "Spherical quadratic equations in free metabelian groups",

abstract = "We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, NP-complete.",

keywords = "Diophantine problem, Free metabelian group, NP-completeness, Quadratic equation",

author = "Igor Lyseno and Alexander Ushakov",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2016",

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doi = "10.1090/proc/12662",

language = "English",

volume = "144",

pages = "1383--1390",

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T1 - Spherical quadratic equations in free metabelian groups

AU - Lyseno, Igor

AU - Ushakov, Alexander

PY - 2016/4

Y1 - 2016/4

N2 - We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, NP-complete.

AB - We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, NP-complete.

KW - Diophantine problem

KW - Free metabelian group

KW - NP-completeness

KW - Quadratic equation

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EP - 1390

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Spherical quadratic equations in free metabelian groups

Abstract

Keywords

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