2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224745We prove that an element $g$ of prime order $>3$ belongs to the solvable radical $R(G)$ of a finite (or, more generally, a linear) group if and only if for every $x\in G$ the subgroup generated by $g, xgx^{-1}$ is solvable. This theorem implies that a finite (or a linear) group $G$ is solvable if and only if in each conjugacy class of $G$ every two elements generate a solvable subgroup.28 pagesGroup Theory20D10; 20D25; 20D06; 20D08text