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Minimal classes and maximal class inp-groups

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Abstract

The number of conjugacy classes of a given size (not 1) in ap-group is divisible byp-1. We study groups in which the number of classes of minimal size is exactlyp-1, and characterise metabelian groups and groups of maximal class with this property.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli, Monte S. Angelo, via Cintia, 80126, Napoli, Italy

    Patrizia Longobardi

  2. Dipartimento di Ingegneria dell'Informazione e Matematica Applicata, Università degli Studi di Salerno, via S. Allende, 84081, Baronissi (Salerno), Italy

    Mercede Maj

  3. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904, Jerusalem, Israel

    Avinoam Mann

Authors
  1. Patrizia Longobardi
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  2. Mercede Maj
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  3. Avinoam Mann
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Additional information

Part of the work of this author was done during his visit to the University of Napoli, under a CNR grant. He is grateful to that university for its hospitality, and also to Y. Berkovich for interesting discussions on the subject matter of this note.

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Longobardi, P., Maj, M. & Mann, A. Minimal classes and maximal class inp-groups. Isr. J. Math. 110, 93–102 (1999). https://doi.org/10.1007/BF02808177

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  • DOI: https://doi.org/10.1007/BF02808177

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