(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that any group with three elements is isomorphic to [tex]Z_{3}[/tex]

2. Relevant equations

3. The attempt at a solution

Let G be the group of three elements

We have an isomorphism if given c:G--->[tex]Z_{3}[/tex],

if c is one-to -one and onto and c(ab)=c(a)c(b)

First, we check one-to-one

We want c(a)=c(b) to imply a=b

My problem here is how to define c(a), c(b).

Onto:

We want c(a)=x and want to solve for a?

c(ab):

Same problem with not knowing what c(ab) is

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# Any group of 3 elements is isomorphic to Z3

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