有限群特征标的 π-次数

The π- Degrees of Characters for Finite Groups

摘要: 设G为任意有限群，N为G的子群，X是G的一个不可约复特征标。记为X(1)的素因子集合。本文给出了X_N的每个不可约分量均有次数的一个条件，推广了Dolfi的相关定理，并给出了若干应用。

Abstract: Let G be a finite group, N a subgroup of G and   X an irreducible complex character of G. Write   to denote the set of prime divisors of  X（1）. The present paper gives a sufficient condition to guarantee that every irreducible constituent of X_N  has  π- degree, which generalizes the corresponding Dolfi’s theorem. Some applications are given.