On Zeros Of Characters Of Finite Groups

It is a classic and important subject to study the structures of finite groups by character theory of finite groups, such as Frobenius's theorem and p aqb-theorem. And there are many meaningful and exicting results by investigating the distribution of zeros in the character tables to characterize finite groups. In this paper, we consider the structures of finite groups by the distribution of zeros in the character tables.It consists of following three chapters:In chapter 1, we introduce some symbols and basic concepts that we usually use in the paper. Moreover, we introduce some backgrounds and results of our research.In chapter 2, we first study the restriction and zeros of characters of finite groups, then, as their application, we simplify the proof of [2, Theorem].In chapter 3, we investigate finite group G with the small number of zero entries outside F (G) in its character table, where F (G) is the Fitting subgroup of G ( the maximal nilpotent normal of G ).At the end of the last two chapters, we leave a series of questions, which are unsolved.