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A conjugacy criterion for Hall subgroups in finite groups

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Abstract

A finite group G is said to satisfy C π for a set of primes π, if G possesses exactly one class of conjugate π-Hall subgroups. We obtain a criterion for a finite group G to satisfy C π in terms of a normal series of the group.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    E. P. Vdovin & D. O. Revin

Authors
  1. E. P. Vdovin
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  2. D. O. Revin
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Correspondence to E. P. Vdovin.

Additional information

Original Russian Text Copyright © 2010 Vdovin E. P. and Revin D. O.

The authors were supported by the Russian Foundation for Basic Research (Grants 10-01-90007, 08-01-00322, and 10-01-00391), the Russian Federal Agency for Education (Grant 2.1.1.419), and the Federal Target Program (State Contract 02.740.11.0429). The first author gratefully acknowledges the support from the Deligne 2004 Balzan Prize in Mathematics and the Lavrent’ev Young Scientists Competition of the Russian Academy of Sciences (Resolution No. 43 of 04.02.2010).

To Yu. L. Ershov on his seventieth birthday.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 506–516, May–June, 2010.

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Vdovin, E.P., Revin, D.O. A conjugacy criterion for Hall subgroups in finite groups. Sib Math J 51, 402–409 (2010). https://doi.org/10.1007/s11202-010-0041-4

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  • DOI: https://doi.org/10.1007/s11202-010-0041-4

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