 Cyclic Group Questions

Subject Mathematics Abstract Algebra

Question

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

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.

Solution Preview

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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...

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