A mixed identity-free elementary amenable group.

A group G is called mixed identity-free if for every n ∈ ℕ and every w ∈ G ∗ F n , there exists a homomorphism φ : G ∗ F n → G such that φ is the identity on G and φ (w) 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. [ABSTRACT FROM AUTHOR]