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 Mat. Zametki, 2005, Volume 78, Issue 1, Pages 125–131 (Mi mz2569)

On the Approximability by Finite $p$-Groups of Free Products of Groups with Normal Amalgamation

E. V. Sokolov

Ivanovo State University

Abstract: A sufficient condition for the residual $p$-finiteness (approximability by the class $\mathscr F_p$ of finite $p$-groups) of a free product $G=(A*B;H)$ of groups $A$ and $B$ with a normal amalgamated subgroup $H$ is obtained. This condition is used to prove that if $A$ and $B$ are extensions of residually $\mathscr N$-groups by $\mathscr F_p$-groups, where $\mathscr N$ stands for the class of finitely generated torsion-free nilpotent groups, and if $H$ is a normal $p'$-isolated polycyclic subgroup, then the group $G$ is residually $p$-finite (i.e., residually $\mathscr F_p$-group), provided the quotient group $G/H^pH'$ is residually $p$-finite.

DOI: https://doi.org/10.4213/mzm2569

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English version:
Mathematical Notes, 2005, 78:1, 114–119

Bibliographic databases:

UDC: 512.543

Citation: E. V. Sokolov, “On the Approximability by Finite $p$-Groups of Free Products of Groups with Normal Amalgamation”, Mat. Zametki, 78:1 (2005), 125–131; Math. Notes, 78:1 (2005), 114–119

Citation in format AMSBIB
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