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XN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 XN has π- degree, which generalizes the corresponding Dolfi’s theorem. Some applications are given.