Orientable quadratic equations in wreath products of abelian groups

Alexander Ushakov; Chloe Weiers

doi:10.1016/j.jalgebra.2026.01.031

Orientable quadratic equations in wreath products of abelian groups

Alexander Ushakov
, Chloe Weiers

Department of Mathematical Sciences

Marymount Manhattan College

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

1 Scopus citations

Abstract

In this paper we study the complexity of solving orientable quadratic equations in wreath products A≀B of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given equation) when the problem is computationally hard or feasible.

Original language	English
Pages (from-to)	324-358
Number of pages	35
Journal	Journal of Algebra
Volume	694
DOIs	https://doi.org/10.1016/j.jalgebra.2026.01.031
State	Published - 15 May 2026

Keywords

Complexity
Diophantine problem
Metabelian groups
NP-completeness
Quadratic equations
Spherical equations
Wreath product

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10.1016/j.jalgebra.2026.01.031

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title = "Orientable quadratic equations in wreath products of abelian groups",

abstract = "In this paper we study the complexity of solving orientable quadratic equations in wreath products A≀B of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given equation) when the problem is computationally hard or feasible.",

keywords = "Complexity, Diophantine problem, Metabelian groups, NP-completeness, Quadratic equations, Spherical equations, Wreath product",

author = "Alexander Ushakov and Chloe Weiers",

note = "Publisher Copyright: {\textcopyright} 2026 Elsevier Inc.",

year = "2026",

month = may,

day = "15",

doi = "10.1016/j.jalgebra.2026.01.031",

language = "English",

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T1 - Orientable quadratic equations in wreath products of abelian groups

AU - Ushakov, Alexander

AU - Weiers, Chloe

PY - 2026/5/15

Y1 - 2026/5/15

N2 - In this paper we study the complexity of solving orientable quadratic equations in wreath products A≀B of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given equation) when the problem is computationally hard or feasible.

AB - In this paper we study the complexity of solving orientable quadratic equations in wreath products A≀B of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given equation) when the problem is computationally hard or feasible.

KW - Complexity

KW - Diophantine problem

KW - Metabelian groups

KW - NP-completeness

KW - Quadratic equations

KW - Spherical equations

KW - Wreath product

UR - https://www.scopus.com/pages/publications/105029035116

UR - https://www.scopus.com/pages/publications/105029035116#tab=citedBy

U2 - 10.1016/j.jalgebra.2026.01.031

DO - 10.1016/j.jalgebra.2026.01.031

M3 - Article

AN - SCOPUS:105029035116

SN - 0021-8693

VL - 694

SP - 324

EP - 358

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Orientable quadratic equations in wreath products of abelian groups

Abstract

Keywords

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