Note: This is the first of “Examples and Counter Examples” series. I plan on expanding such posts in course of time, as I come across examples.

Interesting fact: These are the OEIS lists of number of distinct groups of order n: number of groups,number of abelian groups, number of non-abelian groups

### Examples

1. $\Bbb Z$
2. $\Bbb Q$
3. $\Bbb R$
4. Integers modulo n $\Bbb Z / n \Bbb Z$
5. $S_n,n\le2$, the symmetric group.
6. $A_n \subset S_n,\forall n\ge1$
7. Any group of order < 4

### Counter-Examples (or Non-Abelian Groups)

1. Symmetric groups $S_n,n\ge3$