Abstract:
Let $\mathcal{K}$ be a root class of groups. It is proved that a free product of any family of residually $\mathcal{K}$ groups with one amalgamated subgroup, which is a retract in all free factors, is residually $\mathcal{K}$. The sufficient condition for a generalized free product of two groups to be residually $\mathcal{K}$ is also obtained, provided that the amalgamated subgroup is normal in one of the free factors and is a retract in another.
Keywords:free product with one amalgamated subgroup, root class of groups, root-class residuallity, retract.
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