How close are pth powers in the Nottingham group?
arXiv:math/0207273
Abstract
Let 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 Algebra