Quote:
Originally Posted by MattcAnderson
Not an expert on group theory. But there is the trivial group of just one element. This could be labeled identity or something else. There is no group with count nill.
In my humble opinion the easiest group to understand is cyclic group. These cyclic group must have prime order. .

You acknowledge that you are "Not an expert on group theory".
So why do you feel compelled to post?
Hint: Your claim that a cyclic group must have prime order is wrong.
Further hint: There is a cyclic group of order n for all n \in N.