On the pi-F-norm and the h-F-norm of a finite group
On the pi-F-norm and the h-F-norm of a finite group
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关于有限群的 pi-F-范数和 h-F-范数
DOI：
10.1016/j.jalgebra.2014.01.042
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发表时间：
2014
影响因子：
0.9
通讯作者：
Guo Wenbin
中科院分区：
文献类型：
--
作者：
Chen Xiaoyu;Guo Wenbin
设H是Fitting类，F是群系.我们称有限群G的一个子群NH，F（G）为G的H-F-范数，如果NH，F（G）是G的所有子群的F-剩余之积的正规化子与G的H-根的交.设π表示素数集，G π表示所有有限π-群的类.我们称G的子群NG π，F（G）为G的π F-范数。称G的正规子群N在G中为π F-超中心的，如果N= 1或N> 1，且N之下的每一个G-主因子在G中为F-中心且其阶至少能被π中的一个素数整除.设Z π F（G）表示G的π F-超中心，即G的所有π F-超中心正规子群之积。本文研究了有限群G的H-F-范数，特别是π-F-范数的性质。特别地，我们研究了G的π′ F-范数与π F-超中心之间的关系.
Let H be a Fitting class and F a formation. We call a subgroup N H, F (G) of a finite group G the H–F-norm of G if N H, F (G) is the intersection of the normalizers of the products of the F-residuals of all subgroups of G and the H-radical of G. Let π denote a set of primes and let G π denote the class of all finite π-groups. We call the subgroup N G π, F (G) of G the π F-norm of G. A normal subgroup N of G is called π F-hypercentral in G if either N= 1 or N> 1 and every G-chief factor below N of order divisible by at least one prime in π is F-central in G. Let Z π F (G) denote the π F-hypercentre of G, that is, the product of all π F-hypercentral normal subgroups of G. In this paper, we study the properties of the H–F-norm, especially of the π F-norm of a finite group G. In particular, we investigate the relationship between the π′ F-norm and the π F-hypercentre of G.