I have a small question about groups,
If you have a comunitative 'group' H = <a in H : a2=1>,
Is that enough information to show that it is a group, without knowing the binary operation?
say b is also in H
(a*b)*(b*a) = (a*a)*(b*b) = 1 (since its comunitative)
So that shows there is an identity, and each element is it's own inverse
It's also associative so everything is satisfied for H to be a group,
So only knowing these two properties of this group can show that it is indeed a group?