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On Certain Finitely Generated Subgroups of Groups Which Split
Published online by Cambridge University Press: 20 November 2018
Abstract
Define a group $G$ to be in the class
$S$ if for any finitely generated subgroup
$K$ of
$G$ having the property that there is a positive integer
$n$ such that
${{g}^{n\,}}\in \,K$ for all
$g\,\in \,G,\,K$ has finite index in
$G$. We show that a free product with amalgamation
$A{{*}_{_{C}}}B$ and an
$\text{HNN}$ group
$A{{*}_{C}}$ belong to
$S$, if
$C$ is in
$S$ and every subgroup of
$C$ is finitely generated.
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- Research Article
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- Copyright © Canadian Mathematical Society 2003
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