查询词典 proper subgroup

Let F=LF be a s-closed local formation such that every minimal non-F-groups is solvable. It is proved that 1 If every cyclic subgroup of of order 4 and every minimal subgroup of G are contained in, then G is a F-group. 2 If there exists a normal subgroup N of G such that G/N∈F and every cyclic subgroup of N of order 4 is weakly c-normal in G and every element of N of prime order is contained in Z(superscript f subscript ∞), then G is a F-group.

设F=LF是一个子群闭的局部群系，满足每个极小非F-群是可解群，证明了：1如果G的任意极小子群和任意4阶循环子群都含于Z中，那么G是F-群；2如果存在G的正规子群，使得G/N∈F，且N的任一4阶循环子群在G中弱c-正规，N的任一素数阶元含于Z中，那么G是F-群。

Not every subgroup of a D-group is also a D-group. If a subgroup is a D-group we call the subgroup "sub- D -group." The "commutator ideal" of G is the smallest sub-D-group containing its commutator subgroup. We found that the commutator ideal can be viewed as a finitely generated module over a ring when G is a finitely generated metabelian D-group.

并非每个子群都是一个可除群，若一个子群是可除群，我们称之为子可除群(sub-D-group)，而G 的交换子理想则是在G中包含其导出群的最小子可除群，我们发现当G是一个有限生成亚交换可除群时，其交换子理想是一个有限生成模。

Subgroup H of G is said to be π-quasinormally embedded in G, if for each prime divisor p of the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroup of G.

bstract 设G是有限群，称G的子群H在G中π-拟正规嵌入，如果对于{H}的每个素因子p， H的Sylow p-子群也是G的某个π-拟正规子群的Sylow p-子群。

A subgroup H of G is said to be π-quasinormally embedded in G, if for each prime divisor p of the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some π-quasinormal subgroup of G.

设G是有限群，称G的子群H在G中π-拟正规嵌入，如果对于{H}的每个素因子p， H的Sylow p-子群也是G的某个π-拟正规子群的Sylow p-子群。

A subgroup of a finite group G is called π-quasinormal in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup N of G such that G=HN and H∩N≤H=Core.

有限群G的一个子群称为在G中是π-拟正规的若它与G的每一个Sylow-子群是交换的。G的一个子群H称为在G中是c-可补的若存在G的子群N使得G=HN且H∩N≤H＝Core。

For a finite group G, a subgroup H is called c-normal in G if there is a normal subgroup K such that G=HK and H∩K≤H, the largest normal subgroup of G contained in H. c-normality was replaced by c-π-quasinormality or c-sub-normality. The following were showed equivalent. First, there is a solvable maximal subgroup M such that M is c-π-quasi-normal in G.

推广了有限群中的c-正规性概念，引入了c-次正规性和c-π-拟正规性概念，并利用新概念给出了有限群可解的几个条件，证明了：设G是有限群，那么，下述条件是等价的：G有一个极大子群M在G中是c-π-拟正规的而且是可解的。

Compared the rapid and slow intake rate protocol, the proximal stomach emptying curve is different in non-early satiety subgroup, while there is no difference in the early satiety subgroup.(4) TIV, SIV, TGV, SGV and output volume are significant smaller in early satiety FD subgroup than that in HS, but in non-early satiety FD subgroup only SIV, SGV are significant smaller than HS;(5) If the intake volume is same, the gastric volume is smaller in FD patients;(6) BMI affects the results of LNLT; in HS gender only affect SIV in the slow rate LNLT, in FD gender affect SGV and OV in both rate protocol and SIV in the rapid rate LNLT; age has little effect on the results of LNLT.Ⅲ.

BMI对液体营养餐负荷试验结果存在影响；性别对于HS影响仅可见于慢速饮入速度模式饱足饮入量，对于FD患者饱足饮入量、饱足胃容积及最终排除量、快速饮入速度模式的饱足饮入量均有影响；年龄对于营养餐负荷试验结果影响不大。

Many scholars have studied these respects and given many important results, for example, the Hupperts famous theorem, namely, a finite group G is supersolvable if and only if every maximal subgroup of G has prime index; a finite group G is nilpotent if and only if every maximal subgroup of G is normal in G; a finite group G is solvable if and only if every maximal subgroup of G is c-normal in G (See it in [70]); etc.

很多学者都在这些方面进行了研究，得到了很多重要的结果，如：著名的Huppert定理，即有限群为超可解当且仅当它的所有极大子群的指数为素数；有限群为幂零当且仅当每个极大子群都正规；有限群为可解当且仅当它的极大子群均c-正规(见[70])；等等。

For a Hall π-subgroup in π-separable group and a given π-Fong character, we show that there always exists a normal subgroup, such that some irreducible constituent of this π-Fong character which restricts on the join of these two subgroups is a π-Fong character associated to this normal subgroup.

对于π-可分群的一个Hall π-子群和一个给定的π-Fong特征标，我们证明了总存在一个正规子群使得这个π-Fong特征标在这两个子群的交上的限制的某个不可约成分是联系这个正规子群的一个π-Fong特征标。

The semigroup algebra theory,which has a huge development under interior and exterior double Mathematical conditions form 1950"s to 1960"s,is a new branch of algebra theory.In 1990,R.Biswas gave definition of anti-fuzzy subgroup.In 1995,Shen gave definitions of anti-fuzzy subgroup and normal anti-fiizzy subgroup of group.

半群的代数理论是在数学内部和外部双重条件下，从20世纪50年代到60年代发展起来的一个崭新的代数分支。1990年，Biswas R提出了反Fuzzy子群的定义；1995年沈正维提出了一个群的反Fuzzy子群和正规反Fuzzy子群的定义。

It's not quite as simple as that.

并没有那么容易。

It debuted in 1992 in Japan and the United Kingdom, and 1993 in the United States.

它首次亮相于1992年在日本和英国，在美国1993年。