A mixed identity-free elementary amenable group. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Jacobson, B.
• Is Part Of: Communications in algebra. Volume 49:Issue 1(2021)
• Page Start: 235
• Page End: 241
• Publication Date: 2021-01-02
• Subjects: Geometric group theory -- lacunary hyperbolic groups -- mixed identities; 20F65 -- 20F67; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1797073
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: 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.