Abstract
Let G be a finite group and let ω(G) be the set of its element orders. We prove that if ω(G) = ω(B p (3)) where p is an odd prime, then G ≅ B 3(3) or D 4(3) for p = 3 and G ≅ B p (3) for p > 3.
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Original Russian Text Copyright © 2010 Shen R., Shi W., and Zinov’eva M. R.
The authors were supported by the NNSF of China (Grant 10571128), the SRFDP of China (No. 20060285002), the Doctoral Foundation of Hubei University for Nationalities (Grant MY2009B006), and the Russian Foundation for Basic Research (Grant 07-01-00148).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 2, pp. 303–315, March–April, 2010.
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Shen, R., Shi, W. & Zinov’eva, M.R. Recognition of simple groups B p (3) by the set of element orders. Sib Math J 51, 244–254 (2010). https://doi.org/10.1007/s11202-010-0024-5
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DOI: https://doi.org/10.1007/s11202-010-0024-5