This article is cited in 20 papers

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

E. V. Sokolov, E. A. Tumanova

Ivanovo State University, Ivanovo, Russia

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

Keywords: root class, residual $\pi$-finiteness, root-class residuality, generalized free product.

UDC: 512.543

Received: 12.01.2015

DOI: 10.17377/smzh.2016.57.113

 English version: Siberian Mathematical Journal, 2016, 57:1, 135–144

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