,是正规子群的定义,这意味着 ,从而可以不用区分左右陪集。从而 ,这就是商群的定义——将每个 陪集作为一个元素,记作 。 这件事可以用映射来表达 ,更一般的对于任何映射都可以表示为: ,子群的结构其实是分层的: ,在 的作用下, 。一般教科书上还会给出另外两个同构定理,都可以作为习题自己写出来。
英语解释 (mathematics) a subset (that is not empty) of a mathematical group a distinct and often subordinate group within a group相似短语 stable subgroup 稳定子群 generated subgroup 生成的子群 invariant subgroup 不变子群,正规子群 normal subgroup 不变子群,正规子群 inheader subgroup 头内...
1. Let G be a finite group and K a normal subgroup of Gsuch that K as a group is simple and the square of its order does not divide theorder of G. Prove that if H is a subgroup of G such that H K, then H =K 相关知识点: ...
Thévenaz, J.: Extensions of Group Representations from a Normal Subgroup. Comm. Algebra 11 , 391–425 (1983)Thévenaz, J. (1983) Extensions of group representations from a normal subgroup. Commun. Algebra 11: pp. 391-425J. Thevenaz: Extensions of group representations from a normal ...
1)normal subgroup正规子群 1.Character of group which only have n nontrivialnormal subgroups仅含n个非平凡正规子群的群的特征 2.By using algebra of fixed point class to determine the component factors and properties ofnormal subgroupH of the fundamental group of the covering space, the paper studie...
a distinct and often subordinate group within a group (mathematics) a subset (that is not empty) of a mathematical group 学习怎么用 词组短语 normal subgroup正规子群;不变子群 权威例句 Subgroup Interactions in the Heart and Estrogen/Progestin Replacement Study Lessons Learned ...
How to prove that a subgroup is normal?From a Subgroup to a Group:Let {eq}(G,\cdot) {/eq} be a group (meaning that it is closed on multiplication, associative, it has a neutral, and it has an inverse). Let {eq}S\subset G {/eq} be a subset of G. ...
c-normal subgroupsc-正规子群 1.For example, it is useful to do research about the structure of a group through the use of the properties ofc-normal subgroups、weaklyc-normal subgroupsand weakly quasi-normal.在第3章中,讨论了c-正规、弱c-正规子群的性质,并利用其性质给出一个群为超可解群、可...
a而在抽象代数中,我们研究子群和不变子群,并通过陪集和商群的引入简化其代数结构 But in the abstract algebra, we studies the subgroup and the normal divisor, and simplifies its algebra structure through the coset and the quotient group introduction[translate]...
group is simple if and only if it is isomorphic to all of its non-identity homomorphic images, a finite group is perfect if and only if it has no normal subgroups of prime index, and a group is imperfect if and only if the derived subgroup is not supplemented by any proper normal ...