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On Baer-Suzuki π-theorems

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Abstract

Given a set π of primes, say that the Baer-Suzuki π-theorem holds for a finite group G if only an element of O π(G) can, together with each conjugate element, generate a π-subgroup. We find a sufficient condition for the Baer-Suzuki π-theorem to hold for a finite group in terms of nonabelian composition factors. We show also that in case 2 ∉ π the Baer-Suzuki π-theorem holds for every finite group.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, Russia

    D. O. Revin

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  1. D. O. Revin
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Correspondence to D. O. Revin.

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Original Russian Text Copyright © 2011 Revin D. O.

The author was supported by the Russian Foundation for Basic Research (Grants 08-01-00322, 10-01-00391, and 10-01-90007), the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1/419), the Federal Target Program “Scientific and Educational Personnel of Innovation Russia” for 2009–2013 (State Contracts 02.740.11.5191 and 14.740.11.0346)), and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-3669.2010.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 2, pp. 430–440, March–April, 2011.

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Revin, D.O. On Baer-Suzuki π-theorems. Sib Math J 52, 340–347 (2011). https://doi.org/10.1134/S0037446611020170

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