1) Weakly seminormal
弱半正规
2) weakly quasi-normal
弱拟正规
1.
The main purpose of the present paper is to prove the following some theorems: for a finite group G,if G satisfies one of the following conditions,then G is supersolvable;(1) A maximal and cyclic subgroup of G is weakly quasi-normal in G.
利用弱拟正规子群概念,经推导得到有限群超可解的几个充分条件。
2.
In this paper we discuss the influence on an original finite group G when its Sylow subgroups and other subgroups are weakly quasi-normal,then we obtain some sufficient conditions for supersoluability of group G.
主要讨论了群G的Sylow子群及其他子群的弱拟正规性对群的影响,从而得到原群G超可解的几个充分条件的定理:1)群G有指数为素数的可解正规子群H,若H的每个Sylow子群的极大子群在G中弱拟正规,则G超可解;2)群G有指数为素数的正规子群H,若H的Sylow子群及Sylow子群的2-极大子群皆在G内弱拟正规,则G超可解;3)设G=AB,A超可解,B是P-群,p=maxπ(G),若B与A的极大子群可交换且A弱拟正规于G,则G超可解;4)M为G的幂零极大子群,若M及其极大子群皆在G中弱拟正规,则G超可解。
3) weakly c-normal
弱c-正规
1.
A subgroup H of a finite group G is said to be weakly c-normal in G if there exists a subnormal subgroup K of G such that G = HK and H∩K ≤ HG, where Hq is the maximal normal subgroup of G that is contained in H.
群G的一个子群H称为在G中弱c-正规,若存在G的一个次正规子群K使得G=HK且H∩K≤H_G,其中HG=∩_g∈_GH~9是包含在H中G的最大的正规子群。
2.
A subgroup H of a finite group G is said to be weakly c-normal in G if there exists a subnormal subgroup K of G such that G=HK and H∩K≤ HG,where HG is the maximal normal subgroup of G that is contained in H.
群G的一个子群H称为在G中弱c-正规,若存在G的一个次正规子群K使得G=HK且H∩K≤HG,其中HG=∩g∈GHg是包含在H中G的最大的正规子群。
4) weakly regular *-semigroup
弱正则*-半群
1.
In this paperπ*-semigroup is introduced and prove that a π*-semigroup is a regular semigroup,a π*-semigroups maybe is not an orthodox semigroup,a π*-semigroup maybe is not a weakly regular *-semigroup,exist aπ*-semigroups S we can\'t define a unary operation * on it such that S is a weakly regular *-semigroup.
本文给出了π*-半群的概念,证明了π*-半群是正则半群;π*-半群可以不是纯正半群,可以不是弱正则*-半群。
5) s-seminormal
S-半正规
1.
Finite Groups Whose Maximal Subgroups of Sylow Subgroups are s-seminormal;
Sylow子群的极大子群皆s-半正规的有限群(英文)
2.
On s-seminormal Subgroups of Finite Groups II;
关于有限群的s-半正规子群II(英文)
3.
On s-seminormal Subgroups of Finite Groups I;
关于有限群的s-半正规子群I(英文)
6) Semi-normal
半正规
1.
Some Theorems on Semi-normal Subgrorps;
关于半正规子群的几个定理
2.
By using the c-supplemented or semi-normal properties of minimal subgroups,we present several sufficient conditions for a finite group to be p-nilpotent,which generalize some known results on this topic.
利用极小子群的c-可补性或半正规性,得到有限群成为p-幂零的若干充分条件,推广了已知的几个结果。
3.
In this paper,some sufficient conditons for supersolvability of finite groups are given with the semi-normal properties of the minimal subgroups and Sylow subgroups.
本文利用极小子群及Ｓｙｌｏｗ子群的“半正规”性得到有限群超可解的若干结果其中定理１统一地推广了文［１］，［２］，［４］中几个定理，定理２，３也使文［４］中一些结果得到进一步推广。
补充资料：正规子半群
正规子半群
nonnal sub-semi-group
正规子半群[仪曰司劝一胭‘一，叫p;皿opM~aano压no几yrp”扭a]，半群S的 满足下述条件的子半群H:对任意满足xy‘S的x，y任S‘(记号夕见正规复形(加m司印nlp嫉”和任意h任H，关系xhy〔H与x夕任H等价.5的一个子集是正规子半群，当且仅当在S到某个带单位元的半群(阴n刀一grouP)的满同态下，它是单位元的完全反象.
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条