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Let R be a finite unitary ring whose group of units is not solvable but allgroups of units of all its proper subrings are solvable. In this paper weclassify 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.

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