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The finite p-groups with p conjugacy classes of non-normal subgroups

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Abstract

Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. The finite groups for which ν(G) ≤ 2 were determined by Dedekind and by Schmidt in the early times of group theory. On the other hand, if G is a finite p-group, La Haye and Rhemtulla have proved that either ν(G) ≤ 1 or ν(G) ≥ p. In this note, we determine all finite p-groups satisfying ν(G) = p for p > 2.

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Authors and Affiliations

  1. Matematika Saila, Euskal Herriko Unibertsitatea, 48080, Bilbao, Spain

    Gustavo A. Fernández-Alcober & Leire Legarreta

Authors
  1. Gustavo A. Fernández-Alcober
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  2. Leire Legarreta
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Correspondence to Gustavo A. Fernández-Alcober.

Additional information

Supported by the Spanish Government, grant MTM2008-06680-C02-02/MTM, partly with FEDER funds, and by the Basque Government, grant IT-252-07.

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Fernández-Alcober, G.A., Legarreta, L. The finite p-groups with p conjugacy classes of non-normal subgroups. Isr. J. Math. 180, 189–192 (2010). https://doi.org/10.1007/s11856-010-0100-3

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  • DOI: https://doi.org/10.1007/s11856-010-0100-3

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