A cyclic group is a special kind of group that has many similarities with modular arithmetic.

Task:

A. Prove that the cyclic group of order 3 is a group by doing the following:

1. State each step of your proof.

2. Provide written justification for each step of your proof.

B. Prove that the cyclic group of order 3 is isomorphic to Z3 under addition by doing the following:

1. State each step of your proof.

2. Provide written justification for each step of your proof.

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

The group (Z3,+) has the following elements: {0,1,2}. Addition is done modulo 3. This is an abelian group and it is cyclic with generator 1: 2=1+1, 0=1 + 1 + 1.

Let G be a cyclic group of order 3, with generator g, and elements...

This is only a preview of the solution. Please use the purchase button to see the entire solution