Engel residually finite groups

Question

I know that every finite Engel group is a nilpotent group. Then, if $G$ is a residually finite Engel group, every finite quotient group of $G$ is a nilpotent group. Is necesseraly true that $G$ is a nilpotent group?

Answer 1

The examples by Golod, of groups on $d\geq 3$ generators, whose $(d-1)$-generator subgroups are all nilpotent (see example 18.3.2 in "Fundamentals of the theory of groups" by Kargapolov and Merzljakov for an exposition of the construction and properties) give $p$-groups that are residually finite, Engel, yet not nilpotent.

See this survey by G. Traustason on Engel groups, for other conditions one might add to guarantee nilptency.