On Certain Finitely Generated Subgroups of Groups Which Split

Canadian mathematical bulletin

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

DOI  :  10.4153/CMB-2003-012-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 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.

【 授权许可】

Unknown