Geodesic
On Certain Finitely Generated Subgroups of Groups Which Split
Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 122-129

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DOI

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.
DOI : 10.4153/CMB-2003-012-7
Mots-clés : 20E06, 20E08, 57M07, free product with amalgamation, HNN group, graph of groups, fundamental group 
Moon, Myoungho. On Certain Finitely Generated Subgroups of Groups Which Split. Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 122-129. doi: 10.4153/CMB-2003-012-7
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     title = {On {Certain} {Finitely} {Generated} {Subgroups} of {Groups} {Which} {Split}},
     journal = {Canadian mathematical bulletin},
     pages = {122--129},
     year = {2003},
     volume = {46},
     number = {1},
     doi = {10.4153/CMB-2003-012-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-012-7/}
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