LAUSR

Abstract Every word in a free group F induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on every finite group, necessarily belong to the same orbit of Aut F . A special case of this problem, when one of the words is the primitive word x, was settled positively by the third author and Parzanchevski [15] . Here we extend this result to the case where one of the words is x d or [ x , y ] d for an arbitrary d ∈ Z .