Semidirect product - Wikipedia
In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. It is usually denoted with the symbol ⋉. There are two closely related concepts of semidirect product:
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。
半直积 - 维基百科，自由的百科全书
在 數學 中，特別 抽象代數 裏的 群論 中， 半直積 （英語： 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。 半直積是作為集合的 笛卡爾積，但帶有特定的乘法運算。 令 为群， 为 的一个 正规子群， 是 的一个 子群。 下列命题等价: 存在 同态 ，它的像是 本身而其 核 是 。 如果这些命题中的一个 (从而所有)成立，则称 是一个 和 的 内半直积，或者说 在 上“分裂 (splits)”，并写作 。 若 是其正规子群 和子群 的内半直 …
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. For example, if G is a group of order paqb then the p-Sylow subgroup P and q-Sylow subgroup Q are complementary.
Semidirect products Examples of semidirect products In other words, inside N oH the homomorphism r : H !Aut(N) corresponds to conjugation of N by H. The group N oH is called the semidirect product of N and H. The roles of N and H cannot be exchanged. Example For any cyclic group Z n, there is a homomorphism r : f 1g!Aut(Z n): r( 1)(x) = x: n.
群的半直积 - 知乎 - 知乎专栏
半直积（Semidirect Product） 半直积是群论中的一个重要构造，用于构建更复杂的群结构。 它结合了两个群的性质，并通过一个特定的同态来定义它们之间的作用。
2. Semidirect Products Suppose now we relax the rst condition, so that His still normal in G but Kneed not be. We retain the other conditions, so our conditions are now: (1) His normal in G, (2) H\K= f1g, (3) HK= G, In this case we obtain what is called a semidirect product. Examples: Suppose H ˘=Z=3 and K ˘=Z=2. There is more than one ...
群的半直积 | 中文数学 Wiki | Fandom
在群论中，两个群的半直积（the semidirect product of two groups）是群的直积的推广，它可以借由群作用定义。
2013年6月20日 · Semidirect products are a very useful rudiment of nite group theory, but the diffi-culties in working with them are often both under- and over-estimated. This document attempts to handle some of these issues. A motivating example describe the semi-direct products of …
SEMIDIRECT PRODUCTS KEITH CONRAD 1. Introduction For two groups Hand K, the most basic construction of a group that contains copies of Hand Kas subgroups is the direct product H K, where the group law is componentwise: (h;k)(h0;k0) = (hh0;kk0). Since (h;1)(h0;1) = (hh0;1) and (1;k)(1;k0) = (1;kk0), we can