D. N. Azarov, “On the residual nilpotence of free products of free groups with cyclic amalgamation”, Mat. Zametki, 64:1 (1998), 3–8; Math. Notes, 64:1 (1998), 3

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Matematicheskie Zametki, 1998, Volume 64, Issue 1, Pages 3–8
DOI: https://doi.org/10.4213/mzm1366 (Mi mzm1366)

This article is cited in 15 scientific papers (total in 15 papers)

On the residual nilpotence of free products of free groups with cyclic amalgamation

D. N. Azarov

Ivanovo State University

Full-text PDF (170 kB) Citations (15)

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DOI: https://doi.org/10.4213/mzm1366

Abstract: Let $G$ be a free product of free groups with cyclic amalgamation. In this note we prove a criterion for the group $G$ to be a residually finite $p$-group. Other residual properties of the group $G$ are also established.

Received: 12.07.1996

English version:
Mathematical Notes, 1998, Volume 64, Issue 1, Pages 3–7
DOI: https://doi.org/10.1007/BF02307189

Bibliographic databases:

UDC: 512.543

Language: Russian

Citation: D. N. Azarov, “On the residual nilpotence of free products of free groups with cyclic amalgamation”, Mat. Zametki, 64:1 (1998), 3–8; Math. Notes, 64:1 (1998), 3–7

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1366

https://doi.org/10.4213/mzm1366

https://www.mathnet.ru/eng/mzm/v64/i1/p3

This publication is cited in the following 15 articles:

E.V. Sokolov, “On the residual nilpotence of generalized free products of groups”, Journal of Algebra, 657 (2024), 292
D. N. Azarov, “O pochti moschnosti grupp avtomorfizmov i rasscheplyaemykh rasshirenii”, Sib. matem. zhurn., 64:6 (2023), 1119–1130
D. N. Azarov, “On the Virtual Potency of Automorphism Groups and Split Extensions”, Sib Math J, 64:6 (2023), 1265
D. I. Moldavanskii, “Residual Nilpotence of Groups with One Defining Relation”, Math. Notes, 107:5 (2020), 820–825
E. A. Tumanova, “The root class residuality of the tree product of groups with amalgamated retracts”, Siberian Math. J., 60:4 (2019), 699–708
D. N. Azarov, “A criterion for the $\mathscr F_\pi$-residuality of free products with amalgamated cyclic subgroup of nilpotent groups of finite ranks”, Siberian Math. J., 57:3 (2016), 377–384
A. V. Rozov, E. V. Sokolov, “O nilpotentnoi approksimiruemosti svobodnykh proizvedenii nilpotentnykh grupp s tsentralnymi ob'edinennymi podgruppami”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 6(44), 34–44
Azarov D., “Residual Properties of Generalized Free Products With Cyclic Amalgamation”, Commun. Algebr., 43:4 (2015), 1464–1471
D. N. Azarov, “O finitnoi approksimiruemosti obobschennykh svobodnykh proizvedenii grupp s tsiklicheskim ob'edineniem”, Chebyshevskii sb., 14:3 (2013), 9–19
E. V. Sokolov, “Nekotorye approksimatsionnye svoistva obobschennykh svobodnykh proizvedenii grupp”, Chebyshevskii sb., 13:1 (2012), 143–149
Bou-Rabee Kh., “Parasurface Groups”, Pac. J. Math., 248:1 (2010), 23–30
V. G. Bardakov, R. V. Mikhailov, “On the residual properties of link groups”, Siberian Math. J., 48:3 (2007), 387–394
E. V. Sokolov, “On the Approximability by Finite $p$-Groups of Free Products of Groups with Normal Amalgamation”, Math. Notes, 78:1 (2005), 114–119
E. V. Sokolov, “A Remark on Subgroup Separability in the Class of Finite $\pi$-Groups”, Math. Notes, 73:6 (2003), 855–858
E. V. Sokolov, “On the cyclic subgroup separability of free products of two groups with amalgamated subgroup”, Lobachevskii J. Math., 11 (2002), 27–38

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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