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On the number of conjugacy classes in a finite group II

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Abstract

In this work we obtain new properties connected with the number of conjugacy classes of elements of a finite group, through the analysis of the numberr G(gN) of conjugacy classes of elements ofG that intersect the cosetgN, whereN is a normal subgroup ofG andg any element ofG. The results obtained about this number are not only used in the general problem of classifying finite groups according to the number of conjugacy classes, but they also allow us to improve and generalize known results relating to conjugacy classes due to P. Hall, M. Cartwright, A. Mann, G. Sherman, A. Vera-López and L. Ortíz de Elguea. Examples are given which illustrate our improvements.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, Bilbao, Spain

    Antonio Vera-López & MA Concepción Larrea

  2. Departamento de Matemáticas, Facultad de Económicas, Universidad del País Vasco, Apartado 644, Bilbao, Spain

    Antonio Vera-López & MA Concepción Larrea

Authors
  1. Antonio Vera-López
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  2. MA Concepción Larrea
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This work has been supported by the University of the Basque Country.

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Vera-López, A., Larrea, M.C. On the number of conjugacy classes in a finite group II. Israel J. Math. 64, 87–127 (1988). https://doi.org/10.1007/BF02767372

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  • DOI: https://doi.org/10.1007/BF02767372

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