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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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- Copyright © Canadian Mathematical Society 2003
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