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
DOI: 10.12677/pm.2011.12025, PDF, HTML, 下载: 3,479  浏览: 12,665 
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。
Abstract: 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. 极大子群的h-完备与群的可解性[J]. 理论数学, 2011, 1(2): 124-131. http://dx.doi.org/10.12677/pm.2011.12025

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