2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152775The 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.6 pages. Abstract added in migration.Group TheoryGeometric Topologytext