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. 
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/
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