Geodesic
On the root-class residuality of certain free products of groups with normal amalgamated subgroups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2020), pp. 48-63

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Let $\mathcal{K}$ be a root class of groups closed under taking quotient groups, $G$ be a free product of groups $A$ and $B$ with amalgamated subgroups $H$ and $K$. Let also $H$ be normal in $A$, $K$ be normal in $B$, and $\operatorname{Aut}_{G}(H)$ denote the set of automorphisms of $H$ induced by all inner automorphisms of $G$. We prove a criterion for $G$ to be residually a $\mathcal{K}$-group provided $\operatorname{Aut}_{G}(H)$ is an abelian group or it satisfies some other conditions. We apply this result in the cases when $A$ and $B$ are bounded nilpotent groups or $A/H, B/K \in \mathcal{K}$.
Keywords: generalized free product, residual finiteness, residual $p$-finiteness, residual solvability, root-class residuality. 
@article{IVM_2020_3_a3,
     author = {E. V. Sokolov and E. A. Tumanova},
     title = {On the root-class residuality of certain free products of groups with normal amalgamated subgroups},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--63},
     publisher = {mathdoc},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_3_a3/}
}
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E. V. Sokolov; E. A. Tumanova. On the root-class residuality of certain free products of groups with normal amalgamated subgroups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2020), pp. 48-63. http://geodesic.mathdoc.fr/item/IVM_2020_3_a3/