  In this paper we prove a group theoretic analogue of the well known local
nilpotence theorem for sandwich Lie algebras due to Kostrikin and Zel'manov. We
introduce the notion of a strong left 3-Engel element of a group G and show
that these are always in the locally nilpotent radical of G. This generalises a
previous result of Jabara and Traustason that showed that a left 3-Engel
element a of a group G is in the locally nilpotent radical of G whenever a is
of odd order.
