2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145203We prove that the solvable radical of a finite group G coincides with the set of elements y having the following property: for any x in G the subgroup of G generated by x and y is solvable. We present analogues of this result for finite dimensional Lie algebras and some classes of infinite groups. We also consider a similar problem for pairs of elements.13 pages; completely revised and extended versionGroup Theory20F16text