Subgroups and conjugates in semi-prime rings

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In this paper we obtain results on normal subgroups in semi prime rings which enable us to extend results in [3] on the solvability of normal subgroups and results in [4] on conjugates of noncentral elements. The main tool in our investigation is the recent work of Herstein [2] on the Lie structure of semi prime rings. To use these results we must make an assumption which guarantees a rich supply of elements of square zero, and so, a rich supply of units. Some such assumption is necessary as illustrated by our example in [-4] which shows that even in a prime ring with zero divisors the group of units can be abelian and can centralize noncentral elements, even in the presence of an infinite collection of independent elements of square zero.