On the Residual $\pi$-Finiteness of Generalized Free Products of Groups
Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 605-614.

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

A criterion for the approximability by finite $\pi$-groups of a generalized free product of two finite $\pi$-groups with normal amalgamated subgroups is obtained. Using this criterion, for a generalized free product of two arbitrary groups with normal amalgamation, we find both necessary and sufficient conditions for the residual $\pi$-finiteness that are similar to the Baumslag conditions for the property of residual finiteness. Some applications of this result are indicated.
Keywords: residual finiteness, residual $\pi$-finiteness, generalized free product with normal amalgamation, approximability by finite $\pi$-groups.
@article{MZM_2014_95_4_a10,
     author = {E. A. Tumanova},
     title = {On the {Residual} $\pi${-Finiteness} of {Generalized} {Free} {Products} of {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {605--614},
     publisher = {mathdoc},
     volume = {95},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a10/}
}
TY  - JOUR
AU  - E. A. Tumanova
TI  - On the Residual $\pi$-Finiteness of Generalized Free Products of Groups
JO  - Matematičeskie zametki
PY  - 2014
SP  - 605
EP  - 614
VL  - 95
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a10/
LA  - ru
ID  - MZM_2014_95_4_a10
ER  - 
%0 Journal Article
%A E. A. Tumanova
%T On the Residual $\pi$-Finiteness of Generalized Free Products of Groups
%J Matematičeskie zametki
%D 2014
%P 605-614
%V 95
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a10/
%G ru
%F MZM_2014_95_4_a10
E. A. Tumanova. On the Residual $\pi$-Finiteness of Generalized Free Products of Groups. Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 605-614. http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a10/

[1] G. Baumslag, “On the residual finiteness of generalised free products of nilpotent groups”, Trans. Amer. Math. Soc., 106 (1963), 193–209 | DOI | MR | Zbl

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

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

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

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