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Sufficient conditions for the root-class residuality of certain generalized free products

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Abstract

Given a class K of groups, we prove that the free product of a K -group A and a residually K -group B with amalgamated subgroup which is a retract of B is a residually K -group. We also obtain a sufficient condition for the root-class residuality of a generalized free product of two residually K -groups with amalgamated subgroup which is a retract of one of the factors.

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Correspondence to E. V. Sokolov.

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Ivanovo. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 1, pp. 171–185, January–February, 2016; DOI: 10.17377/smzh.2016.57.113.

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Sokolov, E.V., Tumanova, E.A. Sufficient conditions for the root-class residuality of certain generalized free products. Sib Math J 57, 135–144 (2016). https://doi.org/10.1134/S0037446616010134

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