Geodesic
On a Family of Residually Finite Groups
Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 65-75.

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As is known, there is a finitely generated residually finite group (for short, a residually $\mathcal F$-group) whose extension by some finite group is not a residually $\mathcal F$-group. In the paper, it is shown that, nevertheless, every extension of a finite group by a finitely generated residually $\mathcal F$-group is a Hopf group, and every extension of a center-free finite group by a finitely generated residually $\mathcal F$-group is a residually $\mathcal F$-group. If a finitely generated residually $\mathcal F$-group $G$ is such that every extension of an arbitrary finite group by $G$ is a residually $\mathcal F$-group, then a descending HNN-extension of the group $G$ also has the same property, provided that it is a residually $\mathcal F$-group.
Keywords: residually finite groups, HNN-extensions of groups. 
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D. I. Moldavanskii. On a Family of Residually Finite Groups. Matematičeskie zametki, Tome 105 (2019) no. 1, pp. 65-75. http://geodesic.mathdoc.fr/item/MZM_2019_105_1_a5/

[1] J. M. Corson, Th. J. Ratkovich, “A strong form of residual finiteness for groups”, J. Group Theory, 9 (2006), 497–505 | DOI | MR | Zbl

[2] A. I. Maltsev, “O gomomorfizmakh na konechnye gruppy”, Uchenye zapiski Ivanovskogo ped. in-ta, 18 (1958), 49–60

[3] P. R. Hewitt, “Extensions of residually finite groups”, J. Algebra, 163 (1994), 757–772 | DOI | MR | Zbl

[4] B. Chandler, V. Magnus, Razvitie kombinatornoi teorii grupp. Ocherk istorii razvitiya idei, Mir, M., 1985 | MR | Zbl

[5] A. I. Maltsev, “Ob izomorfnom predstavlenii beskonechnykh grupp matritsami”, Matem. sb., 8 (50):3 (1940), 405–422 | MR | Zbl

[6] S. Meskin, “Nonresidually finite one-relator groups”, Trans. Amer. Math. Soc., 164 (1972), 105–114 | DOI | MR | Zbl

[7] R. Lindon, P. Shupp, Kombinatornaya teoriya grupp, Mir, M., 1980 | MR | Zbl

[8] D. I. Moldavanskii, “Finitnaya approksimiruemost niskhodyaschikh HNN-rasshirenii grupp”, Ukr. matem. zhurn., 44 (1992), 842–845 | MR