一类特殊的p-模Frobenius群
A Special Class of p-Module Frobenius Groups
摘要: 有限群论中著名的Frobenius定理揭示了Frobenius群的内部结构，Frobenius群在有限群及群表示论的研究领域中都起着非常重要的作用。设p为某素数，1996年，Kuisch和Waall类比一般的Frobenius群结构，给出了p-模Frobenius群的定义。本文概述了p-模Frobenius群的常用性质，刻画了一类特殊的p-模Frobenius群的结构。
Abstract:
The famous Frobenius theorem gave the internal structures of Frobenius groups. Frobenius groups have played a very important role in the research field of finite group and group representation theory. Let p be a prime number, in 1996, Kuisch and Waall gave the definition of p-module Fro-benius groups by analogy with Frobenius groups. In this note, several well-known properties and theorems of p-module Frobenius groups are introduced. A special class of p-module Frobenius groups are characterized.
参考文献
|
[1]
|
Isaacs, I.M. (1976) Character Theory of Finite Groups. Academic Press, New York.
|
|
[2]
|
Navarro, G. (1998) Characters and Blocks of Finite Groups. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef]
|
|
[3]
|
Kuisch, E.B. and van der Waall, R.W. (1996) Modular Frobeni-us Groups. Manuscripta Mathematica, 90, 403-427. [Google Scholar] [CrossRef]
|
|
[4]
|
Fan, J., Du, N. and Zeng, J. (2012) The Classification of Some Modular Frobenius Groups. Bulletin of the Australian Mathematical Society, 85, 11-18. [Google Scholar] [CrossRef]
|
|
[5]
|
Fan, J., Du, N. and Zeng, J. (2013) Characterization of Modular Frobenius Groups of Special Type. Acta Mathematica Scientia, 33, 525-531. [Google Scholar] [CrossRef]
|
|
[6]
|
Cao, H.Q. and Zeng, J.W. (2022) A Note on Modular Fro-benius Groups. Journal of Algebra and Its Applications, 21, Article ID: 2250020. [Google Scholar] [CrossRef]
|
|
[7]
|
曹慧芹. 关于强嵌入子群的一些应用[D]: [博士学位论文]. 厦门: 厦门大学, 2020.
|
|
[8]
|
Li, Y., Zeng, J. and Chen, X. (2016) Groups Whose Nonlinear Irreducible Brauer Charac-ters Are Real Valued. Communications in Algebra, 44, 228-239. [Google Scholar] [CrossRef]
|