Geodesic
On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 1, pp. 124-132

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Let $G$ be a free product of residually finite virtually soluble groups $A$ and $B$ of finite rank with an amalgamated subgroup $H$, $H \not= A$ and $H \not= B$. And let $H$ contains a subgroup $W$ of finite index which is normal in both $A$ and $B$. We prove that the group $G$ is residually finite if and only if the subgroup $H$ is finitely separable in $A$ and $B$. Also we prove that if all subgroups of $A$ and $B$ are finitely separable in $A$ and $B$, respectively, all finitely generated subgroups of $G$ are finitely separable in $G$.
Keywords: soluble group of finite rank, generalized free product, residually finite group, finitely separable subgroup. 
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     author = {A. V. Rozov},
     title = {On the {Residual} {Finiteness} of {Some} {Generalized} {Products} of {Soluble} {Groups} of {Finite} {Rank}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {124--132},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2013_20_1_a7/}
}
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A. V. Rozov. On the Residual Finiteness of Some Generalized Products of Soluble Groups of Finite Rank. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 1, pp. 124-132. http://geodesic.mathdoc.fr/item/MAIS_2013_20_1_a7/