Finite unitary rings all of whose groups of units of all their subrings except of the ring itself are solvable.

Let <italic>R</italic> be a finite unitary ring whose group of units is not solvable but all groups of units of all its proper subrings are solvable. In this paper, we classify these rings and show that all finite rings of order pn for n < 5 and some of order p6 are in this class of rings. [ABSTRACT FROM AUTHOR]