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

Abstract

Let R 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 $p^n$ for $n < 5$ and some of order $p^6$ are in this class of rings.