Journal of Combinatorial Algebra

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Volume 1, Issue 3, 2017, pp. 289–340
DOI: 10.4171/JCA/1-3-2

Published online: 2017-07-25

Lie algebras and torsion groups with identity

Efim Zelmanov[1]

(1) University of California – San Diego, La Jolla, USA

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

Keywords: The Burnside problem, pro-$p$ groups, PI-algebras, Lie algebras

Zelmanov Efim: Lie algebras and torsion groups with identity. J. Comb. Algebra 1 (2017), 289-340. doi: 10.4171/JCA/1-3-2