The Levitzki Radical for Omega-groups


A. Buys, G._K. Gerber


The concept locally nilpotent ideal of an $\Omega$-group is defined. The class of locally nilpotent $\Omega$-groups is a Kurosh-Amitsur radical class. Furthermore, the Levitzki radical of an $\Omega$-group is the intersection of all $\Omega$-prime ideals $P$ such that $G/P$ is Levitzki semi-simple.