Raimundo Bastos

On groups admitting a word whose values are Engel

Let m, n be positive integers, v a multilinear commutator word and w = vm. We prove that if G is a residually finite group in which all w-values are n-Engel, then the verbal subgroup w(G) is locally nilpotent. We also examine the question whether this is true in the case where G is locally graded rather than residually finite. We answer the question affirmatively in the case where m = 1. Moreover, we show that if u is a non-commutator word and G is a locally graded group in which all u-values are n-Engel, then the verbal subgroup u(G) is locally nilpotent.

Non-abelian tensor square of finite-by-nilpotent groups

Let G be a group. We denote by

A Sufficient Condition for Nilpotency of the Commutator Subgroup

{\nu(G)}

A criterion for metanilpotency of a finite group

ν(G) an extension of the non-abelian tensor square

Non-abelian tensor product of residually finite groups

{G \otimes G}

On Finite Groups with Few Automorphism Orbits

G⊗G by