weak normality 中文意思是什麼
weak normality
解釋
弱正規性-
It is important to study the structures of finite groups by combining some subgroups with some properties in the researches on finite groups. in this paper, we discuss the following : ( 1 ) the relations between the - pairs of maximal subgroups and c - normality, weak c - normality, s - normality, the normal index of maximal subgroups ; ( 2 ) some results on solvablity of finite groups that are obtained by using the s - normality of subgroups ; ( 3 ) the - pairs of general proper subgroups of finite groups as the generalization of the - pairs of maximal subgroups that is used to describe c - normal subgroups, weak c - normal subgroups and s - normal subgroups, by which some new results on finite groups are obtained ; ( 4 ) some new results on p - quasinilpotent groups and p * - nilpotent groups
本文在前人的基礎上，討論了以下內容： （ 1 ）極大子群的子群偶和c正規性、弱c正規性、 s正規性、正規指數之間的關系； （ 2 ）利用s正規性得到了關于有限群可解性的幾個結果； （ 3 ）將極大子群的子群偶推廣為有限群的一般真子群的偶，證明了有限群的c正規、弱c正規以及s正規子群都可以用一般真子群的偶來描述和幾個新的結果； （ 4 ）研究p擬冪零群和p ~ *冪零群，得到了一些新的結構定理。 -
In this paper, we replace the n normality with n subnormality in c - normal concept to get the weak c - concept. we generalize theorem 3. 4, 3. 5. in [ 1 ]. in this paper, the author gives sufficient and necessary condition of solvable group using the weak c - normality of maximal and sylow subgroup and gets some results about supersolvability and p - nilpotentlity of groups
在這篇文章中，作者研究了弱c -正規的性質並用sylow子群和極大子群的弱c -正規性來確定一些群的結構，給出了一個群為可解群的充分必要條件，同時由極大子群、 sylow子群的弱c -正規性得到群gp -冪零、超可解的有關定理。 -
There has been much interest in the past in investigating the relation between the properties of maximal subgroups of finite group g and the structure of g. in this aspect, the concept of a c - normal subgroup in a finite group was introduced by wang in [ 1 ] and he proved that a finite group is solvable if and only if m is weak c - normal in g for every maximal subgroup m of g. as an application of the above result, some known theorems were generalized by using the concept " c - normality "
有限群g的極大子群和g的結構之間的關系人們已經作了廣泛的研究， 1996年王燕鳴教授在文[ 1 ]中引進了c -正規的概念，在文[ 1 ]中他證明了一個群是可解的當且僅當g的每個極大子群在g中c -正規。作為上面結論的應用，一些重要結論被c -正規的概念加以推廣。
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