Equations over solvable groups | Sciact

Equations over solvable groups Full article

Journal

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Output data

Year: 2024, Volume: 638, Pages: 739-750 Pages count : 12 DOI: 10.1016/j.jalgebra.2023.10.004

Tags

Group theory, Solvable groups, Metabelian groups, Equations over groups, Systems of equations over groups, Group rings, Quasivarieties of groups, Group extensions, Howie conjecture

Authors

Klyachko Anton A. ¹ , Mikheenko Mikhail A. ² , Roman'kov V.A. ^3,4

Affiliations

1	Faculty of Mechanics and Mathematics of Moscow State University, Moscow 119991, Leninskie gory, MSU, Russian Federation
2	Moscow Center for Fundamental and Applied Mathematics, Russian Federation
3	Omsk branch of Sobolev Institute of Mathematics, Omsk 644043, ul. Pevtsova, 13, Russian Federation
4	Dostoevsky Omsk State University

Funding (1)

Russian Science Foundation

22-21-00745

Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with abelian torsion-free quotients has a solution in a larger group with a similar subnormal series of the same length (and an analogous fact is valid for systems of equations).

Klyachko A.A. , Mikheenko M.A. , Roman'kov V.A.
Equations over solvable groups
Journal of Algebra. 2024. V.638. P.739-750. DOI: 10.1016/j.jalgebra.2023.10.004 WOS Scopus РИНЦ OpenAlex

Submitted:	Apr 9, 2023
Published online:	Oct 11, 2023
Published print:	Jan 15, 2024

Web of science:	WOS:001122447500001
Scopus:	2-s2.0-85174457571
Elibrary:	64873463
OpenAlex:	W4387523534

DB	Citing
OpenAlex	3
Scopus	1
Web of science	1
Elibrary	2