Ends of double extension groups (Q1074181)

The author, using the homotopy technique in covering spaces, enlarges the class of groups known to be semistable at \(\infty\) [cf. \textit{B. Jackson}, ibid. 21, 71-81 (1981; Zbl 0472.57001); the author, Trans. Am. Math. Soc. 277, 307-321 (1983; Zbl 0518.57002); J. Pure Appl. Alg. 35, 305-320 (1985)]. His main result: If \(1\to H\to G\to K\to 1\) is a short exact sequence of infinite groups with G finitely presented and H containing a finitely generated, infinite, normal subgroup, then G is 1-ended and semistable at \(\infty\). As an application, it is proved that some class of finitely presented, solvable groups is semistable at \(\infty\).