References
R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer, Berlin (1977).
G. A. Noskov, V. N. Remeslennikov, and V. A. Roman’kov, “Infinite groups,” Itogi Nauki Tekh. Alg., Geom., Topol., 17, 65-157 (1979).
V. N. Remeslennikov and V. A. Roman’kov, “Algorithmic and model theoretic problems in groups,” in Itogi Nauki Tekh. Alg., Geom., Topol., 21, 3-79 (1983).
V. A. Roman’kov, “Equations over groups,” Groups Complex. Cryptol., 4, No. 2, 191-239 (2012).
V. A. Roman’kov, “Unsolvability of the endomorphic reducibility problem in free nilpotent groups and in free rings,” Algebra and Logic, 16, No. 6, 310-320 (1977).
V. A. Roman’kov, “Diophantine questions in the class of finitely generated nilpotent groups,” J. Group Theory, 19, No. 3, 497-514. (2016)
Open Problems in Combinatorial and Geometric Group Theory; www.grouptheory.info.
V. A. Roman’kov, N. G. Khisamiev, and A. A. Konyrkhanova, “Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups,” Sib. Math. J., 58, No. 3, 536-545 (2017).
V. A. Roman’kov, “The commutator width of some relatively free Lie algebras and nilpotent groups,” Sib. Math. J., 57, No. 4, 679-695 (2016).
R. H. Gilman, “Formal languages and infinite groups,” in DIMACS, Ser. Discr. Math. Theor. Comp. Sci., 25, Am. Math. Soc., Providence, RI (1996), pp. 27-51.
V. A. Roman’kov, Rational Subsets in Groups [in Russian], Omsk Univ., Omsk (2014).
A. Myasnikov and V. Roman’kov, “On rationality of verbal subsets in a group,” Theory Comput. Syst., 52, No. 4, 587-598. (2013)
A. Myasnikov and N. Romanovskiy, “Krull dimension of solvable groups,” J. Alg., 324, No. 10, 2814-2831 (2010).
N. S. Romanovskii, “Equational Noetherianness of rigid soluble groups,” Algebra and Logic, 48, No. 2, 147-160 (2009).
C. K. Gupta and N. S. Romanovskii, “The property of being equationally Noetherian for some soluble groups,” Algebra and Logic, 46, No. 1, 28-36 (2007).
N. S. Romanovskii, “Irreducible algebraic sets over divisible decomposed rigid groups,” Algebra and Logic, 48, No. 6, 449-425 (2009).
N. S. Romanovskii, “Coproducts of rigid groups,” Algebra and Logic, 49, No. 6, 539-550 (2010).
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by Russian Science Foundation, project No. 16-11-10002.
Translated from Algebra i Logika, Vol. 56, No. 3, pp. 375-381, May-June, 2017.
Rights and permissions
About this article
Cite this article
Roman’kov, V.A. Solvability of Equations in Classes of Solvable Groups and Lie Algebras. Algebra Logic 56, 251–255 (2017). https://doi.org/10.1007/s10469-017-9445-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10469-017-9445-6