On the number of vanishing conjugacy classes of Frobenius groups
Let G be a finite group and let Irr(G) be the set of all irreducible characters of G. We say that an element g in G is a vanishing element if there exists some character χ ∈ Irr(G) such that χ(g) = 0. We can easily show that the set of vanishing elements of G is the union of some conjugacy classes. In this paper, we obtain the set of vanishing elements of Frobenius groups whose kernel is nilpotent of class 2, and then, we will try to find a suitable lower bound for the number of vanishing conjugacy classes of these groups. Moreover, we will classify Frobenius groups containing at most six vanishing conjugacy classes.
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