Four Objects Groups: Is x^4=e Sufficient?

[yetar]

I know that there are only two four objects groups.
However, I want a term that will be true if and only M is a four objects group.
Will saying that for every x in M, x^4=e will be enought? (Apart from the fact the also a 2 objects group is such a group)
Or is it possible that for every x in M, x^4=e also for groups with more then 4 objects in it?

Thanks in advance.

 

[matt grime]

There are infinitely many groups that satisfy x^4=4 for all x in G: any product of 4-groups for instance.