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Let G be a finite group and S be a finite simple group. In this paper, we prove that if G and S have the same sets of all orders of solvable subgroups, then G is isomorphic to S, or G and S are isomorphic to Bn(q), Cn(q), where n ≥ 3 and q is odd. This gives a positive answer to the problem put forward by Abe and Iiyori.