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Pure Mathematics 2025

在两个群的直积上对有限群特征标余次数的推广
Generalization of the Co-Degree of Characters for Finite Groups on the Direct Product of Two Groups

DOI: 10.12677/pm.2025.153095, PP. 219-224

何满意

Keywords: 有限群，特征标，群直积，特征标余次数
Finite Groups, Characters, Direct Product of Groups, Character Codegrees

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Abstract:

本文旨在推广钱国华老师的特征标余次数。设 $G_{1}$ 和 $G_{2}$ 是两个有限群， $χ_{ξ}, χ_{ζ}$ 分别是 $G_{1}$ 和 $G_{2}$ 的任意不可约特征标，复合得到的特征标 $χ_{ξ} {_{#}}_{ζ}$ 是 $G_{1} \times G_{2}$ 的不可约特征标。我们探讨了 $G_{1} \times G_{2}$ 的特征标余次数 $c o d (χ_{ξ} {_{#}}_{ζ})$ 与 $G_{1}$

References

[1]	Qian, G., Wang, Y. and Wei, H. (2007) Co-Degrees of Irreducible Characters in Finite Groups. Journal of Algebra, 312, 946-955. https://doi.org/10.1016/j.jalgebra.2006.11.001
[2]	卢家宽, 王宇, 张博儒, 等. 有限群不可约特征标的余次数[J]. 广西师范大学学报(自然科学版), 2022, 40(5): 160-167.
[3]	Chillag, D. and Herzog, M. (1990) On character degrees quotients. Archiv der Mathematik, 55, 25-29. https://doi.org/10.1007/bf01199110
[4]	Chillag, D., Mann, A. and Manz, O. (1991) The Co-Degrees of Irreducible Characters. Israel Journal of Mathematics, 73, 207-223. https://doi.org/10.1007/bf02772950
[5]	钱国华. 特征标的算术条件与有限群结构[D]: [博士学位论文]. 武汉: 武汉大学, 2002.
[6]	钱国华. 有限群的特征标与共轭类[D]: [博士学位论文]. 广州: 中山大学, 2007.
[7]	钱国华. 有限群特征标次数商的几点注记[J]. 数学杂志, 2002, 22(2): 217-220.
[8]	邱维声. 群表示论[M]. 北京: 高等教育出版社, 2011: 12.
[9]	钱国华. 有限群的特征标余次数[J]. 数学进展, 2023, 52(1): 1-13.
[10]	南基洙, 王颖. 有限群表示论[M]. 北京: 科学出版社, 2014: 3.
[11]	徐明曜. 有限群导引[M]. 北京: 科学出版社, 1999.
[12]	崔学伟. 两个群之直积的子群与正规子群的结构[J]. 曲阜师院学报(自然科学版), 1984(4): 49-50.
[13]	Isaacs, I.M. (1976) Character Theory of Finite Groups. Academic Press.
[14]	Çinarci, B. (2021) Monomial and Monolithic Characters of Finite Solvable Groups. Bulletin of the Australian Mathematical Society, 105, 440-448. https://doi.org/10.1017/s0004972721000770

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在两个群的直积上对有限群特征标余次数的推广Generalization of the Co-Degree of Characters for Finite Groups on the Direct Product of Two Groups

在两个群的直积上对有限群特征标余次数的推广
Generalization of the Co-Degree of Characters for Finite Groups on the Direct Product of Two Groups