关于阿贝尔Hall π-子群
On Abelian Hall π-Subgroups

作者: 徐 涛 :河北工程大学理学院,河北 邯郸;

关键词: Sylow p-子群Hall &pi-子群&pi-可分群

摘要: 设G是一个有限群,H是G的一个阿贝尔Hall π-子群,则存在g G,使得Oπ= HHg。本文推广了Brodkey的结果。另外讨论了具有阿贝尔Hall π-子群的 π-可分群的性质。

Abstract: Let G be a finite group and H an abelian Hall π-subgroup of G. Then g G, there exists Oπ= HHg such that  . It generalizes Brodkey’s result. In addition, the properties of π-separable groups with Abelian Hall π-subgroup are discussed.

文章引用: 徐 涛 (2015) 关于阿贝尔Hall π-子群。 理论数学, 5, 167-170. doi: 10.12677/PM.2015.55025

参考文献

[1] Robinson, D.J.S. (1996) A course in the theory of groups. 2nd Edition, Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-1-4419-8594-1

[2] Brodkey, J.S. (1963) A note on finite groups with an Abelian Sylow groups. Proceedings of the American Mathematical Society, 14, 132-133.
http://dx.doi.org/10.1090/S0002-9939-1963-0142631-X

[3] 徐明曜(1999) 有限群导引. 科学出版社, 北京.

[4] Isaacs, M.I. (2008) Finite group theory. American Mathematical Society, Providence.
http://dx.doi.org/10.1090/gsm/092

分享
Top