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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
Let $G$ be a finite group and $Ch_i(G)$ some quantitative
sets. In this paper we study the influence of $Ch_i(G)$ to the
structure of $G$. We present a survey of author and his colleagues\
Keywords:characterizable group, element orders, finite simple group; conjugacy class; irreducible character