关于M-群的注记
Notes on M-Groups
DOI: 10.12677/pm.2025.1511285, PDF,    科研立项经费支持
作者: 张洁琳, 高玉婷, 陈晓友*：河南工业大学数学与统计学院，河南 郑州；陈科委：河南工业大学土木建筑学院，河南 郑州
关键词: M-群；可解群；超可解；Sylow子群；M-Group； Solvable Group； Supersolvability； Sylow Subgroup
摘要: 若有限群G的每个不可约(复)特征标均可由子群的线性特征标诱导得到，则G称为M-群。M-群是有限群表示论中重要的研究课题。Huppert证明了，设G有正规可解子群N且G/N为超可解群，若N的Sylow子群是交换的，则G是M-群。本文通过对确定阶数的群进行讨论，利用Huppert定理证明了2024阶群与1892阶群均是M-群。
Abstract: If every irreducible (complex) character of a finite group G can be induced by a linear character of some subgroup, then G is called an M-group, which is an important topic in representation theory of finite groups. Huppert proved that if G has a normal solvable group N with abelian Sylow subgroups such that G/N is supersolvable, then G is an M-group. Groups of determined order are studied in this paper and it is proved that all groups with order 2024 or order 1892 are M-groups by Huppert’s theorem.
文章引用：张洁琳, 高玉婷, 陈晓友, 陈科委. 关于M-群的注记[J]. 理论数学, 2025, 15(11): 239-243. https://doi.org/10.12677/pm.2025.1511285

参考文献

[1] Isaacs, I.M. (1976) Character Theory of Finite Groups. Academic Press.
[2] Dornhoff, L. (1967) M-Groups and 2-Groups. Mathematische Zeitschrift, 100, 226-256. [Google Scholar] [CrossRef] 
[3] Fukushima, H. (2005) Hall Subgroups of M-Groups Need Not Be M-Groups. Proceedings of the American Mathematical Society, 133, 671-675. [Google Scholar] [CrossRef] 
[4] Dade, E.C. (1973) Normal Subgroups of M-Groups Need Not Be M-Groups. Mathematische Zeitschrift, 133, 313-317. [Google Scholar] [CrossRef] 
[5] Loukaki, M. (2001) Normal Subgroups of Odd Order Monomial-Groups. Ph D Dissertation, University of Illinois at Urbana-Champaign.
[6] Lewis, M.L. (2006) M-Groups of Order : A Theorem of Loukaki. Journal of Algebra and Its Applications, 5, 465-503. [Google Scholar] [CrossRef] 
[7] 靳平, 徐茂智. M-群的正规子群[J]. 数学的实践与认识, 2011, 41(10): 244-247.
[8] 陈松良, 石昌梅, 等. 168阶群的完全分类[J]. 贵州师范学院学报, 2019, 35(9): 1-6.
[9] 陈松良, 石昌梅, 等. 120阶群的完全分类[J]. 唐山师范学院学报, 2021, 43(6): 3-6+74.
[10] 李德乐, 曹慧芹. 40阶群和56阶群的同构分类[J]. 厦门大学学报(自然科学版), 2021, 60(1): 58-62.
[11] Isaacs, I.M. (2003) Algebra-A Graduate Course. Mechanical Industry Press.
[12] Isaacs, I M. (2018) Characters of Solvable Groups. American Mathematical Society. [Google Scholar] [CrossRef] 

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