Abstract
It is shown that the condition of nonadjacency of 2 and at least one odd prime in the Gruenberg-Kegel graph of a finite group G under some natural additional conditions suffices to describe the structure of G; in particular, to prove that G has a unique nonabelian composition factor. Applications of this result to the problem of recognition of finite groups by spectrum are also considered.
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Original Russian Text Copyright © 2005 Vasil’ev A. V.
The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00797), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-2069.2003.1), the Program “Development of the Scientific Potential of Higher School” of the Ministry for Education of the Russian Federation (Grant 8294), the Program “Universities of Russia” (Grant UR.04.01.202), and a grant of the Presidium of the Siberian Branch of the Russian Academy of Sciences (No. 86-197).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 511–522, May–June, 2005.
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Vasil’ev, A.V. On Connection Between the Structure of a Finite Group and the Properties of Its Prime Graph. Sib Math J 46, 396–404 (2005). https://doi.org/10.1007/s11202-005-0042-x
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DOI: https://doi.org/10.1007/s11202-005-0042-x