Lie algebras and torsion groups with identity

  • Efim Zelmanov

    University of California – San Diego, La Jolla, USA


We prove that a finitely generated Lie algebra such that (i) every commutator in generators is ad-nilpotent, and (ii) satisfies a polynomial identity, is nilpotent. As a corollary we get that a finitely generated residually- torsion group whose pro- completion satisfies a pro- identity is finite.

Cite this article

Efim Zelmanov, Lie algebras and torsion groups with identity. J. Comb. Algebra 1 (2017), no. 3, pp. 289–340

DOI 10.4171/JCA/1-3-2