Semidirect product - Wikipedia
A semidirect product is a generalization of a direct product of groups, where one group acts on the other. Learn the definitions, examples, properties and generalizations of semidirect products in group theory.
半直积 - 百度百科
在数学中，特别是叫做群论的抽象代数领域中，半直积(semidirect product)是从其中一个是正规子群的两个子群形成一个群的特定方法。 半直积是直积的推广。
A semidirect product is a groups having two complementary subgroups one of which is normal. Definition 10.1. Two subgroups H; K · G are called complementary (to each other) if. H \ K = 1. HK = G [HK = fhk j h 2 H; k 2 Kg]1. For example, if G is a group of order paqb then the p-Sylow subgroup P and q-Sylow subgroup Q are complementary.
Learn about semidirect products of groups, a construction that combines a normal subgroup and a group of automorphisms. See examples, lemmas, and proofs of the only groups of order 6.
半直积 - 维基百科，自由的百科全书
在數學中，特別是叫做群論的抽象代數領域中，半直積(semidirect product)是從其中一個是正規子群的兩個子群形成一個群的特定方法。 半直積是 直積 的推廣。
Semidirect product | Brilliant Math & Science Wiki
Learn about semidirect product, a generalization of direct product in group theory. Find definitions, examples, proofs and applications of inner and outer semidirect products.
4.4 直积与半直积（Direct & Semidirect Product） - 知乎专栏
4.4 直积与半直积（Direct & Semidirect Product） 定义4.21（直积 Direct Product） (i) 令 H,K 为群， H,K 的外直积（external direct product）是群 H\times K ，即 H,K 笛卡尔乘积（cartesian product）生成的集合，有二元关系运算：
Understanding the semidirect product - Mathematics Stack …
2017年4月28日 · The subgroup of $\text{Aut}(S)$ (again, as a set) generated by $G$ and $H$ above is the semidirect product $G \rtimes H$ (regardless of the choice of $s$; exercise). Note the geometric significance of the case $G = \mathbb{R}^n, H = \text{O}(n)$.
Semidirect Product -- from Wolfram MathWorld
6 天之前 · Learn what a semidirect product of groups is, how it differs from a direct product, and how to construct it. See the formula, the references, and the Wolfram|Alpha explorations related to this topic.
Semi-direct product - Encyclopedia of Mathematics
2023年11月23日 · A semi-direct product of groups $A$ and $B$ is a group $G = AB$ that is the product of its subgroups $A$ and $B$, where $B$ is normal in $G$ and $A \\cap B = \\ {1\\}$. …