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OD-Characterization of all simple groups whose
orders are less than 10
ZHANG Liangcai, SHI Wujie
Front. Math. China. 2008, 3 (3): 461-474.
https://doi.org/10.1007/s11464-008-0026-9
Let M be a simple group whose order is less than 108. In this paper, we prove that if G is a finite group with the same order and degree pattern as M, then the following statements hold: (a) If M ≠ A10, U4(2), then G ≅ M; (b) If M = A10, then G ≅ A10 or J2 × Z3; (c) If M = U4(2), then G is isomorphic to a 2-Frobenius group or U4(2). In particular, all simple groups whose orders are less than 108 but A10 and U4(2) are OD-characterizable. As a consequence of this result, we can give a positive answer to a conjecture put forward by W. J. Shi and J. X. Bi in 1990 [Lecture Notes in Mathematics, Vol. 1456, 171–180].
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