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On root-class residuality of generalized free products

D. N. Azarov·D. Tieudjo
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Abstract

Root-class residuality of free product of root-class residual groups is demonstrated. A sufficient condition for root-class residuality of generalized free product $G$ of groups $A$ and $B$ amalgamating subgroups $H$ and $K$ through the isomorphism $ϕ$ is derived. For the particular case when $A=B$, $H=K$ and $ϕ$ is the identity mapping, it is shown that group $G$ is root-class residual if and only if $A$ is root-class residual and subgroup $H$ of $A$ is root-class closed. These results are extended to generalized free product of infinitely many groups amalgamating a common subgroup.

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D. N. Azarov, D. Tieudjo. 2004-08-20. On root-class residuality of generalized free products. https://arxiv.org/abs/math/0408277

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