Which of the following statements are True, and which are False?

Give reasons for your answers.

- There is a finite field of order 45.
- A group G of order 9 has a representation of order 2.
- Every free abelian group is a free group
- Every set is a semi-group.
- If G is an infinite group acting on an infinite set X, then no element of X has finite stabiliser.

**Answer:**

**(5) FALSE:** Let {Z} act on itself by translations: i.e if x is an integer , define