Abstract
Let G be a finite group. An element g ∈ G is called a vanishing element of G if there exists an irreducible complex character χ of G such that χ(g) = 0. The conjugacy class of G containing a vanishing element is called a vanishing class of G. In this paper, we concern on the finite groups G such that the product of every two non-inverse vanishing classes of G is a conjugacy class of G. Also, we study the finite groups G such that product of every two vanishing classes of G which are not inverse modulo the center of G is a conjugacy class of G.
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