Why is the group Z_10 not a free group?

[ehrenfest]

Homework Statement

I don't understand why every group is not free. Apparently Z_10, for example is not a free group. Can someone give me an example of why this group does not satisfy the definition of a free group?

Homework Equations

The Attempt at a Solution

 

[NateTG]

http://mathworld.wolfram.com/FreeGroup.html

$\mathbb{Z}_{10}$
has the relation that
[tex]x^{10}=x^{0}[/itex]<br /> which is not one that is required by the group axioms.[/tex]