# Semistability of amalgamated products, HNN-extensions, and all one-relator groups

@article{Mihalik1992SemistabilityOA, title={Semistability of amalgamated products, HNN-extensions, and all one-relator groups}, author={Michael L. Mihalik and Steven T. Tschantz}, journal={Bulletin of the American Mathematical Society}, year={1992}, volume={26}, pages={131-135} }

The authors announce the following theorem.
Theorem 1. If $G=A*_H B$ is an amalgamated product where $A$ and $B$ are finitely presented and semistable at infinity, and $H$ is finitely generated, then $G$ is semistable at infinity. If $G=A*_H$ is an HNN-extension where $A$ is finitely presented and semistable at infinity, and $H$ is finitely generated, then $G$ is semistable at infinity.

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