A. V. Vasil'ev, M. A. Grechkoseeva, V. D. Mazurov, “Characterization of the finite simple groups by spectrum and order”, Algebra Logika, 2009, Volume 48, Number 6,Pages <nobr>685

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Characterization of the finite simple groups by spectrum and order

A. V. Vasil'ev^ab, M. A. Grechkoseeva^ab, V. D. Mazurov^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: 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, simple group, element orders, recognizability by spectrum and order, symplectic group, orthogonal group.

UDC: 512.542

Received: 05.08.2009