2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121127Using a theorem of J. Groves we give a ping-pong proof of Osin's uniform exponential growth for solvable groups. We discuss slow exponential growth and show that this phenomenon disappears as one passes to a finite index subgroup.minor changes: the connection with the Lehmer conjecture is explicitedGroup TheoryOn uniform exponential growth for solvable groupstext