Solvable Subgroups in Prime Rings

Abstract

Let $R$ be a prime ring with center $Z$ and group of units $U$. The main theorem shows that any solvable normal subgroups of $U$ must lie in $Z$, provided that $R$ is not a domain, $Z$ is large enough, and that the $Z$-subalgebra generated by $U$ contains a nonzero ideal of $R$. One consequence is the determination of the structure of $R$ when $R$ has an involution and the subgroup of $U$ generated by the symmetric units is solvable.