Abstract
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 B n(q), C n(q), where n ⩾ 3 and q is odd. This gives a positive answer to the problem put forward by Abe and Iiyori.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10571128), the National Science Foundation of Jiangsu College and University (Grant No. 03KJB110112) and Suzhou City Senior Talent Supporting Project
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Denecke, K., Li, Xh. & Bi, Jx. A characterization of finite simple groups by the orders of solvable subgroups. SCI CHINA SER A 50, 715–726 (2007). https://doi.org/10.1007/s11425-007-0024-5
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DOI: https://doi.org/10.1007/s11425-007-0024-5