Geodesic
On the Approximability by Finite $p$-Groups of Free Products of Groups with Normal Amalgamation
Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 125-131.

Voir la notice de l'article provenant de la source Math-Net.Ru

A sufficient condition for the residual $p$-finiteness (approximability by the class $\mathscr F_p$ of finite $p$-groups) of a free product $G=(A*B;H)$ of groups $A$ and $B$ with a normal amalgamated subgroup $H$ is obtained. This condition is used to prove that if $A$ and $B$ are extensions of residually $\mathscr N$-groups by $\mathscr F_p$-groups, where $\mathscr N$ stands for the class of finitely generated torsion-free nilpotent groups, and if $H$ is a normal $p'$-isolated polycyclic subgroup, then the group $G$ is residually $p$-finite (i.e., residually $\mathscr F_p$-group), provided the quotient group $G/H^pH'$ is residually $p$-finite. 
@article{MZM_2005_78_1_a11,
     author = {E. V. Sokolov},
     title = {On the {Approximability} by {Finite} $p${-Groups} of {Free} {Products} of {Groups} with {Normal} {Amalgamation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {125--131},
     publisher = {mathdoc},
     volume = {78},
     number = {1},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a11/}
}
TY  - JOUR
AU  - E. V. Sokolov
TI  - On the Approximability by Finite $p$-Groups of Free Products of Groups with Normal Amalgamation
JO  - Matematičeskie zametki
PY  - 2005
SP  - 125
EP  - 131
VL  - 78
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a11/
LA  - ru
ID  - MZM_2005_78_1_a11
ER  - 
%0 Journal Article
%A E. V. Sokolov
%T On the Approximability by Finite $p$-Groups of Free Products of Groups with Normal Amalgamation
%J Matematičeskie zametki
%D 2005
%P 125-131
%V 78
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a11/
%G ru
%F MZM_2005_78_1_a11
E. V. Sokolov. On the Approximability by Finite $p$-Groups of Free Products of Groups with Normal Amalgamation. Matematičeskie zametki, Tome 78 (2005) no. 1, pp. 125-131. http://geodesic.mathdoc.fr/item/MZM_2005_78_1_a11/

[1] Maltsev A. I., “O gomomorfizmakh na konechnye gruppy”, Uchen. zap. Ivanovskogo gos. ped. in-ta, 18 (1958), 49–60

[2] Allenby R. B. J. T., Gregorac R. J., “On locally extended residually finite groups”, Lecture Notes in Math., 319, 1973, 9–17 | MR | Zbl

[3] Higman G., “Amalgams of $p$-groups”, J. Algebra, 1 (1964), 301–305 | DOI | MR | Zbl

[4] Sokolov E. V., “Ob approksimiruemosti konechnymi $p$-gruppami nekotorykh svobodnykh proizvedenii s ob'edinennoi podgruppoi”, Chebyshevskii sb., 3:1 (2002), 97–102 | MR | Zbl

[5] Sokolov E. V., “Zamechanie ob otdelimosti podgrupp v klasse konechnykh $\pi$-grupp”, Matem. zametki, 73:6 (2003), 904–909 | MR | Zbl

[6] Sokolov E. V., Ob otdelimosti tsiklicheskikh podgrupp v svobodnykh proizvedeniyakh dvukh grupp s ob'edinennoi podgruppoi, Dep. VINITI 12.07.2002 No. 1325-V2002, Ivanovskii gos. un-t, Ivanovo, 2002

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

[8] Kim G., Tang C. Y., “On generalized free products of residually finite $p$-groups”, J. Algebra, 201 (1998), 317–327 | DOI | MR | Zbl

[9] Sokolov E. V., “On the cyclic subgroup separability of free products of two groups with amalgamated subgroup”, Lobachevskii J. Math., 11 (2002), 27–38 | MR | Zbl

[10] Yakushev A. V., “Approksimiruemost konechnymi $p$-gruppami rasscheplyayuschikhsya rasshirenii grupp”, Nauchn. trudy Ivanovskogo gos. un-ta. Matem., 2000, no. 3, 119–124