Geodesic
Characterization of the finite simple groups by spectrum and order
Algebra i logika, Tome 48 (2009) no. 6, pp. 685-728.

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We give an affirmative answer to Question 12.39 in the Kourovka Notebook. Namely, it is proved that a finite simple group and a finite group having equal orders and same sets of element orders are isomorphic.
Keywords: finite group, element orders, recognizability by spectrum and order, symplectic group
Mots-clés : simple group, orthogonal group. 
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A. V. Vasil'ev; M. A. Grechkoseeva; V. D. Mazurov. Characterization of the finite simple groups by spectrum and order. Algebra i logika, Tome 48 (2009) no. 6, pp. 685-728. http://geodesic.mathdoc.fr/item/AL_2009_48_6_a0/

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