On Certain Finitely Generated Subgroups of Groups Which Split

[摘要] Define a group $G$ to be in the class $mathcal{S}$ if for anyfinitely generated subgroup $K$ of $G$ having the property thatthere is a positive integer $n$ such that $g^n in K$ for all$gin G$, $K$ has finite index in $G$. We show that a freeproduct with amalgamation $A*_C B$ and an $HNN$ group $A *_C$ belongto $mathcal{S}$, if $C$ is in $mathcal{S}$ and every subgroup of$C$ is finitely generated.

[学科分类] 数学（综合）

[关键词] free product with amalgamation;$HNN$ group;graph of groups;fundamental group