理论数学

Vol.1 No.2 (July 2011)

极大子群的h-完备与群的可解性
On h-Completion for Maximal Subgroups and the Solvability of Finite Groups

 

作者:

张晓燕 , 徐伟华

 

关键词:

有限群θ-完备h-完备可解性Finite Group h-Completion Solvability

 

摘要:

本文给出了有限群G极大子群M h-完备的定义,即称C为M的h-完备,若C是M的θ-完备,且有C = G或存在G的一个子群D使得D不是M的θ-完备,但有C < D成立. 从而,可以通过这个定义把θ-完备的极大性削弱,并得到了有关群可解性的重要结论,丰富了有限群理论。

In this paper, we propose new definition of an h-completion for a maximal subgroup M of a group G, that is a θ-completion C such that either C = G or there exist a subgroup D of G which is not a θ-completion for M and C < D holds. This method can weaken the imposed maximality on θ-completion. Moreover, we studied the solvability and of finite groups by means of h-completion and obtained some important properties, which are very useful to research deeply finite groups.

文章引用:

张晓燕 , 徐伟华 (2011) 极大子群的h-完备与群的可解性。 理论数学, 1, 124-131. doi: 10.12677/pm.2011.12025

 

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