- #1

- 45

- 0

## Homework Statement

Show that any group of order 4 or less is abelian

**2. The attempt at a solution**

I came across this hint.

Since its of order 4 we have {e,a,b,c}, where e = identity.

The elements a, b, c must have order 2 or 4. There are two possibilities.

1. a, b, c all have order 2.

2. At least one of them, say a, has order 4.

Why does the elements a, b, c have order 2 or 4? And why does at least one of them have order 4?