This article is cited in 5 papers

A criterion for the $\mathscr F_\pi$-residuality of free products with amalgamated cyclic subgroup of nilpotent groups of finite ranks

D. N. Azarov

Ivanovo State University, Ivanovo, Russia

Abstract: Let $G$ be the free product of nilpotent groups $A$ and $B$ of finite rank with amalgamated cyclic subgroup $H$, $H\ne A$ and $H\ne B$. Suppose that, for some set $\pi$ of primes, the groups $A$ and $B$ are residually $\mathscr F_\pi$, where $\mathscr F_\pi$ is the class of all finite $\pi$-groups. We prove that $G$ is residually $\mathscr F_\pi$ if and only if $H$ is $\mathscr F_\pi$-separable in $A$ and $B$.

Keywords: generalized free product, nilpotent group, residual finiteness, finite $p$-group.

UDC: 512.543

Received: 11.05.2015

DOI: 10.17377/smzh.2016.57.301

 English version: Siberian Mathematical Journal, 2016, 57:3, 377–384

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