A remark on a formula of Zassenhaus (Q1176554)

The authors recently related groups of coalgebra morphisms to some formulas of Zassenhaus involving products of exponentials in a completed free associative algebra [Geom. Dedicata 35, No. 1-3, 177-191 (1990; Zbl 0699.16009)]. Here they relate their methods to the original identity of Zassenhaus for positive characteristic \(p\). In doing so, they obtain a simple proof of a theorem of Baues concerning expressions of the form \(x_ 1^{p^ n}+\dots+x_ r^{p^ n}-(x_ 1+\dots+x_ r)^{p^ n}\) in a free associative algebra on \(x_ 1,\dots,x_ r\).