On Residually Finite Groups with Engel-like Conditions. Issue 10 (2nd October 2016) - Bastos, Raimundo
Abstract : Let m, n be positive integers. Suppose that G is a residually finite group in which for every element x  ∈  G there exists a positive integer q  =  q ( x ) ≤  m such that x q is left n -Engel. We show that G is locally virtually nilpotent. Further, let w be a multilinear commutator and G a residually finite group in which for every product of at most 896 w -values x there exists a positive integer q  =  q ( x ) dividing m such that x q is left n -Engel. Then w ( G ) is locally virtually nilpotent.