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Structure of normal subgroups with three G-class sizes

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Abstract

Let G be a finite group and N be a normal subgroup of G. Suppose that the set of G-conjugacy class sizes of N is {1, m, n}, with m < n and m does not divide n. In this paper, we show that N is solvable, and we determine the structure of these subgroups.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Jaume I, 12071, Castellón, Spain

    A. Beltrán

  2. Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 46022, Valencia, Spain

    M. J. Felipe

  3. Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 15914, Tehran, Iran

    Z. Akhlaghi & M. Khatami

Authors
  1. Z. Akhlaghi
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  2. A. Beltrán
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  3. M. J. Felipe
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  4. M. Khatami
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Corresponding author

Correspondence to A. Beltrán.

Additional information

Communicated by John S. Wilson.

A. Beltrán and M. J. Felipe are supported by Proyecto MTM2007-68010-C03-03, by Proyecto MTM2010-19938-C03-02 and by Proyecto GV-2009-021. A. Beltrán is also supported by grant Fundació Caixa-Castelló P11B2008-09.

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Akhlaghi, Z., Beltrán, A., Felipe, M.J. et al. Structure of normal subgroups with three G-class sizes. Monatsh Math 167, 1–12 (2012). https://doi.org/10.1007/s00605-011-0290-8

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  • DOI: https://doi.org/10.1007/s00605-011-0290-8

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