Geodesic
A Remark on Subgroup Separability in the Class of Finite $\pi$-Groups
Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 904-909 
E. V. Sokolov. A Remark on Subgroup Separability in the Class of Finite $\pi$-Groups. Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 904-909. http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a11/
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     author = {E. V. Sokolov},
     title = {A {Remark} on {Subgroup} {Separability} in the {Class} of {Finite} $\pi${-Groups}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that if a group $G$ is residually $\mathscr N$, then for every $\mathscr N$-subgroup of the group $G$, the set of $\pi'$-roots from this subgroup is a $\pi$-separable $\mathscr N$-subgroup.

[1] Maltsev A. I., “O gomomorfizmakh na konechnye gruppy”, Uchenye zapiski Ivan. gos. ped. in-ta, 18 (1958), 49–60 | Zbl

[2] Kholl F., “Nilpotentnye gruppy”, Matematika. Periodicheskii sbornik perevodov inostrannykh statei, no. 1, Mir, M., 1968, 3–36

[3] Baumslag G., “On the residual nilpotence of certain one-relator groups”, Comm. Pure Appl. Math., 21:5 (1968), 491–506 | DOI | MR | Zbl

[4] Azarov D. N., “O nilpotentnoi approksimiruemosti svobodnykh proizvedenii svobodnykh grupp s tsiklicheskim ob'edineniem”, Matem. zametki, 64:1 (1998), 3–8 | MR | Zbl

[5] Loginova E. D., “Finitnaya approksimiruemost svobodnogo proizvedeniya dvukh grupp s kommutiruyuschimi podgruppami”, Sib. matem. zh., 40:2 (1999), 395–407 | MR | Zbl