2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64608Let F be a field of characteristic p > 0 and let g, h be elements of the Nottingham group N(F) such that g has depth k and gh^{-1} has depth n >= k. We find the best possible lower bound for the depth of g^ph^{-p}.15 pages, LaTeX. Submitted to Journal of AlgebraGroup Theory20E18text