Geodesic
On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups
Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 767-780.

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Let $\mathcal{C}$ be an arbitrary class of groups which has the root property, consists of finite groups only, and contains at least one nonidentity group. It is proved that every extension of a free group by a $\mathcal{C}$-group is conjugacy $\mathcal{C}$-separable. It is also proved that, if $G$ is a free product of two conjugacy $\mathcal{C}$-separable groups with finite amalgamated subgroup or an HNN-extension of a conjugacy $\mathcal{C}$-separable group with finite associated subgroups, then the group $G$ is residually $\mathcal{C}$ if and only if it is conjugacy $\mathcal{C}$-separable.
Keywords: class of groups which has the root property, HNN-extension, free product with finite amalgamated subgroup, residually $\mathcal{C}$ group, conjugacy $\mathcal{C}$-separable group. 
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E. V. Sokolov. On the Conjugacy Separability of Some Free Constructions of Groups by Root Classes of Finite Groups. Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 767-780. http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a10/

[1] P. F. Stebe, “A residual property of certain groups”, Proc. Amer. Math. Soc., 26 (1970), 37–42 | DOI | MR | Zbl

[2] J. L. Dyer, “Separating conjugates in free-by-finite groups”, J. London Math. Soc. (2), 20:2 (1979), 215–221 | DOI | MR | Zbl

[3] E. A. Ivanova, O nilpotentnoi approksimiruemosti obobschennykh svobodnykh proizvedenii grupp, Dis. $\dots$ kand. fiz.-matem. nauk, Ivanovskii gos. un-t, Ivanovo, 2004

[4] E. A. Ivanova, “Ob approksimiruemosti otnositelno sopryazhennosti konechnymi $p$-gruppami svobodnykh proizvedenii dvukh grupp s ob'edinennoi podgruppoi”, Matem. zametki, 76:4 (2004), 502–509 | DOI | MR | Zbl

[5] E. A. Ivanova, “Approksimiruemost otnositelno sopryazhennosti konechnymi $p$-gruppami svobodnykh proizvedenii dvukh grupp”, Vestn. Ivanovsk. gos. un-ta. Ser. “Biologiya, Khimiya, Fizika, Matematika”, 2005, no. 3, 83–91

[6] K. W. Gruenberg, “Residual properties of infinite soluble groups”, Proc. London Math. Soc. (3), 7 (1957), 29–62 | DOI | MR | Zbl

[7] D. V. Goltsov, N. I. Yatskin, “Klassy grupp i podgruppovye topologii”, Vestn. Ivanovsk. gos. un-ta. Ser. “Estestvennye, obschestvennye nauki”, 2011, no. 2, 115–128

[8] H. Neumann, “Generalized free products with amalgamated subgroups. II”, Amer. J. Math., 31:3 (1949), 491–540 | DOI | MR | Zbl

[9] A. Karrass, D. Solitar, “Subgroups of HNN groups and groups with one defining relations”, Canad. J. Math., 23 (1971), 627–543 | DOI | MR | Zbl

[10] J. L. Dyer, “Separating conjugates in amalgamated free products and HNN extensions”, J. Austral. Math. Soc. Ser. A, 29:1 (1980), 35–51 | DOI | MR | Zbl

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

[12] A. Karrass, D. Solitar, “The subgroups of a free product of two groups with an amalgamated subgroups”, Trans. Amer. Math. Soc., 150 (1970), 227–255 | DOI | MR | Zbl

[13] G. P. Scott, “An embedding theorem for groups with a free subgroups of finite index”, Bull. Lond. Math. Soc., 6 (1974), 304–306 | DOI | MR | Zbl

[14] V. Magnus, A. Karrass, D. Soliter, Kombinatornaya teoriya grupp. Predstavlenie grupp v terminakh obrazuyuschikh i sootnoshenii, Nauka, M., 1974 | MR | Zbl