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

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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/}
}
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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/