有限群特征标的 π-次数
The π- Degrees of Characters for Finite Groups

作者: 张月明 * , 靳 平 :山西大学数学科学学院;

关键词: 不可约特征标 π-次数次正规子群Irreducible Character π- Degree Subnormal Subgroup

摘要: G为任意有限群,NG的子群,XG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 Dolfis theorem. Some applications are given.

文章引用: 张月明 , 靳 平 (2012) 有限群特征标的 π-次数。 理论数学, 2, 164-167. doi: 10.12677/PM.2012.23026

参考文献

[1] I. M. Isaacs. Character theory of finite groups. New York: Academic Press, 1994.

[2] I. M. Isaacs. Constituents of restricted and induced characters in odd order groups. Journal of Algebra, 1995, 178(3): 991-1001.

[3] S. Dolfi. A note on character restrictions. Communications in Algebra, 2002, 30(7): 3429-3434.

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