有限群特征标的 π-次数
The π- Degrees of Characters for Finite Groups
DOI: 10.12677/PM.2012.23026, PDF, HTML,    国家自然科学基金支持
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: 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.
文章引用：张月明, 靳平. 有限群特征标的 π-次数[J]. 理论数学, 2012, 2(3): 164-167. http://dx.doi.org/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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