# Finite group of size n for each n > 1 example

So I am trying to think of an example of a finite group of size $$n$$ for each $$n \gt 1$$, but nothing is coming to mind.

If it is a finite group denoted as $$G$$, then the order of G is is $$|G|$$, but I can't think of a group that satisfies this. I am just stuck and I am not sure if I am not understanding the question.

• Every group satisfies this for some $n$. You just need, given some arbitrary $n$, to find a group that satisfies it for that particular $n$. There's one obvious example. For a hint, if $n$ is prime, there is exactly one group of that order: generalise those. – user3482749 Nov 30 '18 at 14:59
• I don't see the obvious example. I am still trying to understand this. Is there anyway you can be more explicit. I am new to abstract algebra – Hawaiian Rolls Nov 30 '18 at 15:35
• Wait, would $\mathbb{Z}_3$ work? Since $|\mathbb{Z}_n| = n$? – Hawaiian Rolls Nov 30 '18 at 15:38
• Yes, $\mathbb{Z}_n$ will work for any $n$. It's a group, it has order $n$. – user3482749 Nov 30 '18 at 15:40

$$\mathbb{Z}/n \mathbb{Z}$$
• Can you explain your answer. This is what I am getting from your answer. That if n = 2, then the size of G would be $\pm \frac{1}{2}$ which has two elements? I am new to abstract algebra so I apologize for not understanding this immediately. – Hawaiian Rolls Nov 30 '18 at 15:29
• $\mathbb{Z}/n\mathbb{Z}$ is a common notation for what you're calling $\mathbb{Z}_n$. – user3482749 Nov 30 '18 at 15:40