Abstract
We describe the finitely generated groups that are universally equivalent to the solvable Baumslag–Soliter group with parameters \( (1,n) \), \( |n|>1 \).
Similar content being viewed by others
References
Chapuis O., “Universal theory of certain solvable groups and bounded Ore group rings,” J. Algebra, vol. 176, no. 2, 368–391 (1995).
Chapuis O., “\( \forall \)-Free metabelian groups,” J. Symb. Log., vol. 62, no. 1, 159–174 (1997).
Romanovskii N. S., “Universal theories for free solvable groups,” Algebra Logic, vol. 51, no. 3, 259–263 (2012).
Romanovskii N. S., “On the universal theories of generalized rigid metabelian groups,” Sib. Math. J., vol. 61, no. 5, 878–883 (2020).
Gupta Ch. K. and Timoshenko E. I., “Partially commutative metabelian groups: centralizers and elementary equivalence,” Algebra Logic, vol. 48, no. 3, 173–192 (2009).
Baumslag G., Myasnikov A., and Remeslennikov V., “Algebraic geometry over groups. I. Algebraic sets and ideal theory,” J. Algebra, vol. 219, no. 1, 16–79 (1999).
Romanovskii N. S., “Equational Noethericity of metabelian \( r \)-groups,” Sib. Math. J., vol. 61, no. 1, 154–158 (2020).
Romanovskii N. S., “Decomposition of a group over an Abelian normal subgroup,” Algebra Logic, vol. 55, no. 4, 315–326 (2016).
Funding
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0001. Structure, Representations and Algorithmic Problems of Groups and Algebras).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 1, pp. 197–201. https://doi.org/10.33048/smzh.2022.63.113
Rights and permissions
About this article
Cite this article
Romanovskii, N.S. Groups Universally Equivalent to the Solvable Baumslag–Soliter Group. Sib Math J 63, 163–166 (2022). https://doi.org/10.1134/S003744662201013X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S003744662201013X