  In this note we further explore the properties of universal enveloping
algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus
expansion, we analyze the properties of group like-elements belonging to
(suitable completions) of those Hopf algebras. Of particular interest is the
case of post-Lie algebras defined in terms of solutions of modified classical
Yang-Baxter equations. In this setting we will study factorization properties
of the aforementioned group-like elements.
