In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that = () where the group operation …

本文，我们将讨论 群论中最重要的概念——群同态(group homomorphism)了，它被广泛应用于数学和物理等领域。 如果有两个群—— G 和 H ，如何对两者进行比较？

群同态（group homomorphism）是群论中两个群之间保持群乘法结构的一种映射。 即群同态为保持群乘法结构的映射。 群映射到自身的群同态是 自同态。 同时为 满射 的群同态是 满同态， …

在群论中， 群同态 （group homomorphism）是关于 群 的函数的 同态。 若一个从群 映至群 的 映射 具有以下性质 则称 为 到 的一个群同态。 若一个群同态的映射 为双射，则其为一 群 同构 …

5 天之前 · A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f (g_1g_2)=f (g_1)f (g_2) for all g_1,g_2 in G, where the product on the …

2021年10月10日 · Definition 2.4.1. Group homomorphism. Let \(G,H\) be groups. A map \(\phi\colon G\to H\) is called a homomorphism if \[\phi(xy) = \phi(x)\phi(y) \nonumber \] for all …

DEFINITION: A group homomorphism is a map G ! H between groups that satisfies. (g1 g2) = (g1) (g2). DEFINITION: An isomorphism of groups is a bijective homomorphism. DEFINITION: …

2024年8月8日 · Let (G,o) & (G’,o’) be 2 groups, a mapping “f ” from a group (G,o) to a group (G’,o’) is said to be a homomorphism if – f(aob) = f(a) o' f(b) ∀ a,b ∈ G The essential point here …

Let \phi:G \rightarrow \bar G be a homomorphism, and let H be a subgroup of G. Then \phi(H) = \{\phi(h)|h \in H\} is a subgroup of \bar G; If H is cyclic, then \phi(H) is cyclic. If H is Abelian, …

A homomorphism between groups \((G, \cdot)\) and \((H, \circ)\) is a map \(\phi :G \rightarrow H\) such that \[ \phi( g_1 \cdot g_2 ) = \phi( g_1 ) \circ \phi( g_2 ) \nonumber \] for \(g_1, g_2 \in …