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On zeros of characters of finite groups

Jinshan Zhang; Zhencai Shen; Dandan Liu — 2010

Czechoslovak Mathematical Journal

For a finite group $G$ and a non-linear irreducible complex character $χ$ of $G$ write $υ (χ) = {g \in G ∣ χ (g) = 0}$ . In this paper, we study the finite non-solvable groups $G$ such that $υ (χ)$ consists of at most two conjugacy classes for all but one of the non-linear irreducible characters $χ$ of $G$ . In particular, we characterize a class of finite solvable groups which are closely related to the above-mentioned question and are called solvable $ϕ$ -groups. As a corollary, we answer Research Problem $2$ in [Y. Berkovich and L. Kazarin: Finite...

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