Abstract
Considering the partially commutative groups of the varieties that include the variety of all length 2 nilpotent groups, we study the questions of factor cancellation in direct products, coincidence of elementary theories, characterization of the group by its elementary theory, and the possibility of direct product decomposition.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Szmielew W., “Elementary properties of Abelian groups,” Fund. Math., vol. 41, no. 2, 203–271 (1955).
Kharlampovich O. and Myasnikov A., “Elementary theory of free non-abelian groups,” J. Algebra, vol. 302, 451–552 (2006).
Sela Z., “Diophantine geometry over groups. VI. The elementary theory of free group,” Geom. Funct. Anal., vol. 16, no. 3, 707–730 (2006).
Romanovskii N. S. and Timoshenko E. I., “On some elementary properties of soluble groups of derived length 2,” Sib. Math. J., vol. 44, no. 2, 350–354 (2003).
Kim K. H., Makar-Limanov L., Neggers J., and Roush F. W., “Graph algebras,” J. Algebra, vol. 64, 46–51 (1980).
Droms C., “Isomorphisms of graph groups,” Proc. Amer. Math. Soc., vol. 100, 407–408 (1987).
Gupta Ch. K. and Timoshenko E. I., “Partially commutative metabelian groups: centralizers and elementary equivalence,” Algebra and Logic, vol. 48, no. 3, 173–192 (2009).
Oger F., “Cancellation and elementary equivalence of finitely generated finite-by-nilpotent groups,” J. London Math. Soc. (2), vol. 44, no. 1, 173–183 (1991).
Hirshon R., “Some cancellation theorems with application to nilpotent groups,” J. Austral Math. Soc. (Ser. A), vol. 23, no. 2, 147–165 (1977).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Dedicated to Academician Yuri Leonidovich Ershov on the occasion of his 80th birthday.
Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 681–686.
The authors were partially supported by the Mathematical Center in Akademgorodok under Agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.
Rights and permissions
About this article
Cite this article
Romanovskii, N.S., Timoshenko, E.I. Elementary Equivalence and Direct Product Decompositions of Partially Commutative Groups of Varieties. Sib Math J 61, 538–541 (2020). https://doi.org/10.1134/S0037446620030167
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446620030167