A mixed identity-free elementary amenable group

Abstract

A group G is called mixed identity-free if for every and every there exists a homomorphism such that is the identity on G and is nontrivial. In this paper, we make a modification to the construction of elementary amenable lacunary hyperbolic groups provided by Ol’shanskii et al. to produce finitely generated elementary amenable groups which are mixed identity-free. As a byproduct of this construction, we also obtain locally finite p-groups which are mixed identity-free.