1 research outputs found
A 5-Engel associative algebra whose group of units is not 5-Engel
Let R be an associative ring with unity and let [R] and U(R) denote the
associated Lie ring (with [a,b]=ab-ba) and the group of units of R,
respectively. In 1983 Gupta and Levin proved that if [R] is a nilpotent Lie
ring of class c then U(R) is a nilpotent group of class at most c. The aim of
the present note is to show that, in general, a similar statement does not hold
if [R] is n-Engel. We construct an algebra R over a field of characteristic
different from 2 and 3 such that the Lie algebra [R] is 5-Engel but U(R) is not
a 5-Engel group.Comment: 9 pages, Corollary 1.4 and some references adde