maximal subgroup造句
例句与造句
- for a maximal subgroup m of a finite group g the normal index of m is the order of a chief factor h / k where h is minimal in the set of supplements of m in g . in this paper we can obtain some results about solvability and supersolvability by using the normal indexes of maximal subgroups of finite groups
有限群g的极大子群m的正规指数是指g的主因子hk的阶，其中h为m在g中的极小正规补。本文利用正规指数的概念，获得有限群可解，超可解的若干结果。 - for a maximal subgroup m of a finite group g the normal index of m is the order of a chief factor h / k where h is minimal in the set of supplements of m in g . in this paper we can obtain some results about solvability and supersolvability by using the normal indexes of maximal subgroups of finite groups
有限群g的极大子群m的正规指数是指g的主因子hk的阶，其中h为m在g中的极小正规补。本文利用正规指数的概念，获得有限群可解，超可解的若干结果。 - then g is solvable if and only if there exists a solvable s-normal maximal subgroup m of g; 3 ) let g be a finite group and mo = 1 where m is a maximal subgroup of g . then g is solvable if and only if m is a supersolvable s-normal subgroup of g and | g : m | = r where r is a prime
则g可解当且张新建:关于有限群的s一止规子群仅当g有一个可解s一正规极大子群m;3)设g为有限群，m为g的极大子群且mg=l。则g可解当且仅当m为g的超可解s一正规子群且}g:m=r其中r为素数。 - then g is solvable if and only if there exists a solvable s-normal maximal subgroup m of g; 3 ) let g be a finite group and mo = 1 where m is a maximal subgroup of g . then g is solvable if and only if m is a supersolvable s-normal subgroup of g and | g : m | = r where r is a prime
则g可解当且张新建:关于有限群的s一止规子群仅当g有一个可解s一正规极大子群m;3)设g为有限群，m为g的极大子群且mg=l。则g可解当且仅当m为g的超可解s一正规子群且}g:m=r其中r为素数。 - 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
本文在前人的基础上，讨论了以下内容：(1)极大子群的子群偶和c正规性、弱c正规性、s正规性、正规指数之间的关系；(2)利用s正规性得到了关于有限群可解性的几个结果；(3)将极大子群的子群偶推广为有限群的一般真子群的偶，证明了有限群的c正规、弱c正规以及s正规子群都可以用一般真子群的偶来描述和几个新的结果；(4)研究p拟幂零群和p~*幂零群，得到了一些新的结构定理。 - It's difficult to find maximal subgroup in a sentence. 用maximal subgroup造句挺难的
- 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
本文在前人的基础上，讨论了以下内容：(1)极大子群的子群偶和c正规性、弱c正规性、s正规性、正规指数之间的关系；(2)利用s正规性得到了关于有限群可解性的几个结果；(3)将极大子群的子群偶推广为有限群的一般真子群的偶，证明了有限群的c正规、弱c正规以及s正规子群都可以用一般真子群的偶来描述和几个新的结果；(4)研究p拟幂零群和p~*幂零群，得到了一些新的结构定理。 - 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
本文在前人的基础上，讨论了以下内容：(1)极大子群的子群偶和c正规性、弱c正规性、s正规性、正规指数之间的关系；(2)利用s正规性得到了关于有限群可解性的几个结果；(3)将极大子群的子群偶推广为有限群的一般真子群的偶，证明了有限群的c正规、弱c正规以及s正规子群都可以用一般真子群的偶来描述和几个新的结果；(4)研究p拟幂零群和p~*幂零群，得到了一些新的结构定理。 - note that the subnormal conditions are weaker than that of normality, we try to use the subnormal conditions replace the normal conditions . it follows that s-normality of a group is defined . using s-normality of maximal subgroups, sylow subgroups and the maximal subgroups of sylow subgroups, we determine the structures of some groups
考虑到次正规的条件比正规的条件弱，我们用次正规的条件代替正规的条件，从而引进了s-正规子群的概念，并运用sylow子群、sylow子群的极大子群、极大子群的s-正规性确定一些群的结构，从而将许多已有的结论进行了推广。 - note that the subnormal conditions are weaker than that of normality, we try to use the subnormal conditions replace the normal conditions . it follows that s-normality of a group is defined . using s-normality of maximal subgroups, sylow subgroups and the maximal subgroups of sylow subgroups, we determine the structures of some groups
考虑到次正规的条件比正规的条件弱，我们用次正规的条件代替正规的条件，从而引进了s-正规子群的概念，并运用sylow子群、sylow子群的极大子群、极大子群的s-正规性确定一些群的结构，从而将许多已有的结论进行了推广。 - in 1, we give main definitions and basic results that are needed in the paper . in 2, we determine the structures of some groups by using s-normality of sylow subgroups and the maximal subgroups of sylow subgroups . there are the main theorems that 1 ) let g be a finite group and p be a sylow p-subgroup of g where p is a prime divisor of | g |
我们在1中将给出本文所需的主要概念和基本结果，在2中讨论sylow子群、sylow子群的极大子群的s-正规性对群的结构的影响，主要结果是1)设g为有限群，p为|g|的素因子，p为g的sylowp-子群。 - 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的极大子群和g的结构之间的关系人们已经作了广泛的研究，1996年王燕鸣教授在文[1]中引进了c-正规的概念，在文[1]中他证明了一个群是可解的当且仅当g的每个极大子群在g中c-正规。作为上面结论的应用，一些重要结论被c-正规的概念加以推广。 - 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的极大子群和g的结构之间的关系人们已经作了广泛的研究，1996年王燕鸣教授在文[1]中引进了c-正规的概念，在文[1]中他证明了一个群是可解的当且仅当g的每个极大子群在g中c-正规。作为上面结论的应用，一些重要结论被c-正规的概念加以推广。 - in l, the author gives main definitions and basic results what are needed in the paper . in 2, the author determines the structures of some groups by using s-normality of sylow subgroups and the maximal subgroups of sylow subgroups . there are the main theorems that 1 ) a group g is metanilpotent if and only if every sylow subgroup of g is s normal in g
我们在1中将给出本文所需的主要概念和基本结果，在2中讨论sylow子群、sylow子群的极大子群的s-正规性对群的结构的影响，主要结论是1)群g是亚幂零的当且仅当g的每个sylow子群在g中s-正规。 - in chapter 1, one type of maximal subgroups in symplectic groups over polynomial rings are obtained . let f be a field, r = f [ x ] be a ring of polynomial in one variable over f, m be a positive integer, f ef and s be the ideal of r generated by-f, we define :, then g ( s ) is a maximal subgroups of sp ( 2m, r )
在第一章中，得到了多项式环上辛群的一类极大子群：设f是一个域，r=f[]是域f上关于的一元多项式环，m是一个正整数，ff，s是r的由-f生成的理想，则是sp(2m，r)的一个极大子群。 - in chapter 1, one type of maximal subgroups in symplectic groups over polynomial rings are obtained . let f be a field, r = f [ x ] be a ring of polynomial in one variable over f, m be a positive integer, f ef and s be the ideal of r generated by-f, we define :, then g ( s ) is a maximal subgroups of sp ( 2m, r )
在第一章中，得到了多项式环上辛群的一类极大子群：设f是一个域，r=f[]是域f上关于的一元多项式环，m是一个正整数，ff，s是r的由-f生成的理想，则是sp(2m，r)的一个极大子群。