Some Characterizations About Frobenius Groups

Frobenius theorem is one of the two celebrated applications of character theory of the finite groups. This theorem was proved in the beginning of the 20st and led many researchers to study Frobenius groups. After long periods of research, people find that Frobenius groups have strong properties, they play an important role in the character theory of finite groups and have great influences on the structure of finite groups.In this paper, we will give further characterizations of Frobenius groups. In Chapter one, we give some preliminaries, mainly including some definitions and lemmas. In Chapter two, we introduce some important properties of Frobenius groups by the abstract group theory. And in Chapter three, we characterize the Frobenius groups by the character theory of finite groups.