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On Certain Finitely Generated Subgroups of Groups Which Split

Published online by Cambridge University Press:  20 November 2018

Myoungho Moon
Myoungho Moon*
Affiliation:
Department of Mathematics Education, Konkuk University, Seoul 143-701, Korea, e-mail: mhmoon@kkucc.konkuk.ac.kr
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Abstract

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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.

Keywords

20E0620E0857M07free product with amalgamationHNN groupgraph of groupsfundamental group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 122 - 129
Copyright
Copyright © Canadian Mathematical Society 2003

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