Free 𝐸-𝑚 groups and free 𝐸-𝑚 semigroups

Abstract

A group [semigroup] is called E E - m m if it satisfies the identity ( x y ) m = x m y m {(xy)^m} = {x^m}{y^m} . In this paper the author studies a necessary and sufficient condition on m m and n n for the free E E - m m group [semigroup] to be homomorphic onto the free E  -  n E{\text { - }}n group [semigroup].