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-Lopez and L. Ortiz de Elguea. Examples are given which illustrate our improvements.
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