On the separability of subgroups of nilpotent groups by root classes of groups

References

[1] D. N. Azarov, On the residual finiteness of free products of solvable minimax groups with cyclic amalgamated subgroups, Math. Notes 93 (2013), no. 3–4, 503–509. 10.1134/S0001434613030188Search in Google Scholar

[2] D. N. Azarov, On the residual finiteness of generalized free products of finite rank groups, Sib. Math. J. 54 (2013), no. 3, 379–387. 10.1134/S0037446613030014Search in Google Scholar

[3] D. N. Azarov, A criterion for the F π -residuality of free products with an amalgamated cyclic subgroup of nilpotent groups of finite ranks, Sib. Math. J. 57 (2016), no. 3, 377–384. 10.1134/S0037446616030010Search in Google Scholar

[4] V. G. Bardakov, On D. I. Moldavanskii’s question about 𝑝-separable subgroups of a free group, Sib. Math. J. 45 (2004), no. 3, 416–419. 10.1023/B:SIMJ.0000028606.51473.f7Search in Google Scholar

[5] V. G. Bardakov, On 𝑝-separability of subgroups of free metabelian groups, Algebra Colloq. 13 (2006), no. 2, 289–294. 10.1142/S1005386706000253Search in Google Scholar

[6] F. Berlai, Residual properties of free products, Comm. Algebra 44 (2016), no. 7, 2959–2980. 10.1080/00927872.2015.1065858Search in Google Scholar

[7] F. Berlai and M. Ferov, Separating cyclic subgroups in graph products of groups, J. Algebra 531 (2019), 19–56. 10.1016/j.jalgebra.2019.05.001Search in Google Scholar

[8] P. A. Bobrovskii and E. V. Sokolov, The cyclic subgroup separability of certain generalized free products of two groups, Algebra Colloq. 17 (2010), no. 4, 577–582. 10.1142/S1005386710000556Search in Google Scholar

[9] A. E. Clement, S. Majewicz and M. Zyman, The Theory of Nilpotent Groups, Birkhäuser, Cham, 2017. 10.1007/978-3-319-66213-8Search in Google Scholar

[10] K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. Lond. Math. Soc. (3) 7 (1957), 29–62. 10.1112/plms/s3-7.1.29Search in Google Scholar

[11] M. Hall, Jr., A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950), 575–581. 10.1090/S0002-9939-1950-0038336-7Search in Google Scholar

[12] A. Karrass and D. Solitar, The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227–255. 10.1090/S0002-9947-1970-0260879-9Search in Google Scholar

[13] A  D. Logan, The residual finiteness of (hyperbolic) automorphism-induced HNN-extensions, Comm. Algebra 46 (2018), no. 12, 5399–5402. 10.1080/00927872.2018.1468904Search in Google Scholar

[14] E. D. Loginova, Residual finiteness of the free product of two groups with commuting subgroups, Sib. Math. J. 40 (1999), no. 2, 341–350. 10.1007/s11202-999-0013-8Search in Google Scholar

[15] R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Ergeb. Math. Grenzgeb. (3) 89, Springer, Berlin, 1977. Search in Google Scholar

[16] W. Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), no. 1, 259–280. 10.1007/BF01472217Search in Google Scholar

[17] A. I. Mal’cev, On homomorphisms onto finite groups (in Russian), Ivanov. Gos. Ped. Inst. Ucen. Zap. 18 (1958), 49–60; translation in Transl. Amer. Math. Soc. (2) 119 (1983), 67–79. Search in Google Scholar

[18] D. I. Moldavanskii, On the separability of cyclic subgroups in the direct product of groups (in Russian), Vestn. Ivanov. Gos. Univ. 18 (2017), 83–93. Search in Google Scholar

[19] D. J. S. Robinson, A Course in the Theory of Groups, Grad. Texts in Math. 80, Springer, New York, 1996. 10.1007/978-1-4419-8594-1Search in Google Scholar

[20] J.-P. Serre, Trees, Springer, Berlin, 1980. 10.1007/978-3-642-61856-7Search in Google Scholar

[21] E. V. Sokolov, On the cyclic subgroup separability of the free product of two groups with commuting subgroups, Internat. J. Algebra Comput. 24 (2014), no. 5, 741–756. 10.1142/S0218196714500313Search in Google Scholar

[22] E. V. Sokolov, A characterization of root classes of groups, Comm. Algebra 43 (2015), no. 2, 856–860. 10.1080/00927872.2013.851207Search in Google Scholar

[23] E. V. Sokolov, Separability of the subgroups of residually nilpotent groups in the class of finite 𝜋-groups, Sib. Math. J. 58 (2017), no. 1, 169–175. 10.1134/S0037446617010219Search in Google Scholar

[24] E. V. Sokolov, The root-class residuality of the fundamental groups of certain graphs of groups with central edge subgroups, Sib. Math. J. 62 (2021), no. 6, 1119–1132. 10.1134/S0037446621060136Search in Google Scholar

[25] E. V. Sokolov, Certain residual properties of HNN-extensions with central associated subgroups, Comm. Algebra 50 (2022), no. 3, 962–987. 10.1080/00927872.2021.1976791Search in Google Scholar

[26] E. V. Sokolov and E. A. Tumanova, Sufficient conditions for the root-class residuality of some generalized free products, Sib. Math. J. 57 (2016), no. 1, 135–144. 10.1134/S0037446616010134Search in Google Scholar

[27] E. V. Sokolov and E. A. Tumanova, Root class residuality of HNN-extensions with central cyclic associated subgroups, Math. Notes 102 (2017), no. 4, 556–568. 10.1134/S0001434617090280Search in Google Scholar

[28] E. V. Sokolov and E. A. Tumanova, Generalized direct products of groups and their application to the study of residuality of free constructions of groups, Algebra Logic 58 (2020), no. 6, 480–493. 10.1007/s10469-020-09568-xSearch in Google Scholar

[29] E. V. Sokolov and E. A. Tumanova, On the root-class residuality of certain free products of groups with normal amalgamated subgroups, Russ. Math. 64 (2020), 43–56. 10.3103/S1066369X20030044Search in Google Scholar

[30] E. A. Tumanova, On the root class residuality of Baumslag–Solitar groups, Sib. Math. J. 58 (2017), no. 3, 546–552. 10.1134/S003744661703017XSearch in Google Scholar

[31] E. A. Tumanova, The root class residuality of the tree product of groups with amalgamated retracts, Sib. Math. J. 60 (2019), no. 4, 699–708. 10.1134/S0037446619040153Search in Google Scholar