Group homomorphism

From Maths

(Redirected from Homomorphism (group))

Jump to: navigation, search

Stub grade: A

This page is a stub

This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:

Demote to grade D once it's been fleshed out a bit, got references. The content is okay for now, it's accurate I promise.

Definition

A group homomorphism is a function, $f:G\rightarrow H$ between two groups, $(G,\times)$ and $(H,*)$ such that:

$\forall a,b\in G[f(a\times b)=f(a)*f(b)]$

These are homomorphisms in the categorical sense (of the $\mathrm{GROUP}$ category)

References

v • d • e Group theory

Overview of the basic and important objects of group theory - a branch of abstract algebra

Primitives	semigroup $\supset$ monoid $\supset$ group $\supset$ Abelian group (AKA: commutative group), group action

Morphisms	Group homomorphism, Group isomorphism

Subobjects	subgroup, normal subgroup, cosets

Important theorems	First isomorphism theorem, second isomorphism theorem, third isomorphism theorem (overview of the group isomorphism theorems)

Important groups	Symmetric group (Permutation group), Alternating group, Dihedral group, Quaternion group, Klein-4 group

Retrieved from "http://www.maths.kisogo.com/index.php?title=Group_homomorphism&oldid=2738"

Hidden categories:

Navigation menu