I need to prove that the cyclic group of order 3 is a
group showing each step with written...

Question

I need to prove that the cyclic group of order 3 is a
group showing each step with written justification.I also need to prove that it isisomorphic to Z3 under addition showing
each stop with written justification.

David · Accepted Answer

SOLUTION: 
A group is an algebraic structure consisting of a set and an operation 
defined on it which satisfies the following four properties: 
1) Closure 
2) Associativity 
3) Identity 
4) Invertibility
To show: the cyclic group of order 3 is a group.
Proof:
A cyclic group of order 3 is a group consisting of a set of 3 elements 
{1=  , x,   } under the operation ( . ) such that         (   )     .
Now we see that for any r and s , ( r+s )mod3 lies in the set {0,1,2} 
. Hence for any           belonging to the group,         (   )      
always lies in the set {1, x,   } and hence is a member of the group. 
Hence the closure property is satisfied.
Now take any              belonging to the group. 
(     ).

I need to prove that the cyclic group of order 3 is a group showing each step with written justification.I also need to prove that it isisomorphic to Z 3 under addition showing each stop with written...

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