Abstract:
Let G be a free product of almost soluble groups A and B of finite rank with amalgamated normal subgroup H, where H≠A and H≠B, and let π be a finite set of primes. We prove that G is an almost residually finite π-group if and only if so are A,B,A/H, and B/H.
Citation:
D. N. Azarov, “Approximability of generalized free products of groups with amalgamated normal subgroup by some classes of finite groups”, Sibirsk. Mat. Zh., 56:2 (2015), 249–264; Siberian Math. J., 56:2 (2015), 206–216
\Bibitem{Aza15}
\by D.~N.~Azarov
\paper Approximability of generalized free products of groups with amalgamated normal subgroup by some classes of finite groups
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 2
\pages 249--264
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\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 2
\pages 206--216
\crossref{https://doi.org/10.1134/S0037446615020020}
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Linking options:
https://www.mathnet.ru/eng/smj2636
https://www.mathnet.ru/eng/smj/v56/i2/p249
This publication is cited in the following 7 articles:
D. R. Baranov, E. V. Sokolov, “On the Separability of Abelian Subgroups of the Generalized Free Product of Two Groups with Normal Amalgamated Subgroup”, Sib Math J, 66:2 (2025), 262
E.V. Sokolov, “On the residual nilpotence of generalized free products of groups”, Journal of Algebra, 657 (2024), 292
D. N. Azarov, “On the virtual potency of some groups and free constructions”, Siberian Math. J., 63:6 (2022), 1023–1033
E. V. Sokolov, E. A. Tumanova, “On the root-class residuality of certain free products of groups with normal amalgamated subgroups”, Russian Math. (Iz. VUZ), 64:3 (2020), 43–56
D. N. Azarov, “On the weak π-potency of some groups and free products”, Siberian Math. J., 61:6 (2020), 953–962
A. E. Kuvaev, E. V. Sokolov, “Necessary conditions of the approximability of generalized free products and
HNN-extensions”, Russian Math. (Iz. VUZ), 61:9 (2017), 32–42
D. V. Goltsov, “Approksimiruemost fundamentalnoi gruppy konechnogo grafa grupp kornevym klassom grupp”, Chebyshevskii sb., 17:3 (2016), 64–71
Citation in format AMSBIB
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