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Abnormality Criteria for p-Complements

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Algebra and Logic Aims and scope

It is proved that for any finite group G possessing a p-complement H for some prime number p, the following assertions are equivalent: (1) all p-complements of G are self-normalizable; (2) all p-complements of G are abnormal; (3) the subgroup H is abnormal in G; (4) NG(HX) = HX for any \( X\underline{\vartriangleleft}\;G \); (5) G does not contain central chief p-factors.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    E. P. Vdovin & D. O. Revin

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, 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.

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Supported by International Mathematical Center of Novosibirsk State University.

Translated from Algebra i Logika, Vol. 55, No. 5, pp. 531-539, September-October, 2016.

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Vdovin, E.P., Revin, D.O. Abnormality Criteria for p-Complements. Algebra Logic 55, 347–353 (2016). https://doi.org/10.1007/s10469-016-9406-5

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