2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166173We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.20 pagesGroup Theory20E05; 05C25text