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.