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On Certain Finitely Generated Subgroups of Groups Which Split |
Canad. Math. Bull. 46(2003), 122-129
Published:2003-03-01
Printed: Mar 2003
Printed: Mar 2003
- Myoungho Moon
Abstract
Define a group $G$ to be in the class $\mathcal{S}$ 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 $\HNN$ group $A *_C$ belong
to $\mathcal{S}$, if $C$ is in $\mathcal{S}$ and every subgroup of
$C$ is finitely generated.
| Keywords: | free product with amalgamation, $\HNN$ group, graph of groups, fundamental group |
| MSC Classifications: |
20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20E08 - Groups acting on trees [See also 20F65] 57M07 - Topological methods in group theory |