Groups which satisfy a Thue–Morse identity.

In this paper, we study 3-Thue–Morse groups, but these are the groups satisfying the semigroup identity x y 2 x y x 2 y = y x 2 y x y 2 x. We prove that if G is a 3-Thue–Morse group then 〈 x , x y 〉 is soluble for every x and y in G. Furthermore, if G is an Engel group without involution then we show that G is locally nilpotent. [ABSTRACT FROM AUTHOR]