Solvable subgroups in prime rings

Abstract

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