A mixed identity-free elementary amenable group

  title={A mixed identity-free elementary amenable group},
  author={Brian Jacobson},
  journal={Communications in Algebra},
  pages={235 - 241}
  • B. Jacobson
  • Published 13 December 2019
  • Mathematics
  • Communications in Algebra
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. 

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