# Groups

Submitted by Structure on Sun, 11/25/2007 - 19:42.

Definition

Let G be a set and a binary operation.

Suppose has properties

Then couple is called group.

If

is called a commutative group.

For a more simple notation we write

Then group axioms become

Commutativity

Group morphism

Let and a function.

f is called morphism of groups if

or with the other notation