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Finite groups with real conjugacy classes of prime size

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Abstract

We determine the structure of a finite group G whose noncentral real conjugacy classes have prime size. In particular, we show that G is solvable and that the set of the sizes of its real classes is one of the following: {1}, {1, 2}, {1, p}, or {1, 2, p}, where p is an odd prime.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Firenze, 50134, Firenze, Italy

    Silvio Dolfi

  2. Dipartimento di Matematica, Università degli Studi di Milano, 20133, Milano, Italy

    Emanuele Pacifici

  3. Departament d’Álgebra, Facultat de Matemàtiques, Universitat de València, 46100, Burjassot, Valéncia, Spain

    Lucia Sanus

Authors
  1. Silvio Dolfi
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  2. Emanuele Pacifici
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  3. Lucia Sanus
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Corresponding author

Correspondence to Silvio Dolfi.

Additional information

The first and second authors are partially supported by MIUR project “Teoria dei Gruppi e Applicazioni”.

The third author is partially supported by the Ministerio de Educación y Ciencia, MTM2007-61161.

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Dolfi, S., Pacifici, E. & Sanus, L. Finite groups with real conjugacy classes of prime size. Isr. J. Math. 175, 179–189 (2010). https://doi.org/10.1007/s11856-010-0008-y

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  • DOI: https://doi.org/10.1007/s11856-010-0008-y

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