SM-vanishing conjugacy classes of finite groups.

Let G be a finite group. In this paper, we say that g ∈ G is an SM-vanishing element of G, if there exists a strongly monolithic character χ of G such that χ(g) = 0. The conjugacy class of an SM-vanishing element of G is called an SM-vanishing conjugacy class of G. Our purpose here is to prove that for determining some properties of the structure of the group G, it is enough to consider the same arithmetical conditions on the sizes of SM-vanishing conjugacy classes of G instead of certain arithmetical conditions on the sizes of vanishing conjugacy classes of G. [ABSTRACT FROM AUTHOR]