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The {ie210-01}-property in finite simple groups

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Abstract

Let π be some set of primes. A finite group is said to possess the {ie210-02}-property if all of its maximal π-subgroups are conjugate. It is not hard to show that this property is equivalent to satisfaction of the complete analog of Sylow's theorem for Hall π-subgroups of a group. In the paper, we bring to a close an arithmetic description of finite simple groups with the {ie210-03}-property, for any set π of primes. Previously, it was proved that a finite group possesses the {ie210-04}-property iff each composition factor of the group has this property. Therefore, the results obtained mean in fact that the question of whether a given group enjoys the {ie210-05}-property becomes purely arithmetic.

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    D. O. Revin

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Correspondence to D. O. Revin.

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Supported by RFBR (grant No. 08-01-00322), by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1), and by SB RAS (Integration project No. 2006.1.2)

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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 364–394, May–June, 2008.

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Revin, D.O. The {ie210-01}-property in finite simple groups. Algebra Logic 47, 210–227 (2008). https://doi.org/10.1007/s10469-008-9010-4

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  • DOI: https://doi.org/10.1007/s10469-008-9010-4

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