Given the four Cayley diagrams in the attachment, one needs to determine which of the groups represented by them are isomorphic.
The Attempt at a Solution
Well, after inspecting all of them, I concluded none are isomorphic.
For the first two, after constructing the tables, one can find a product where the identity elements don't coincide. The same with the third one and the first two. Now, the fourth diagram, unless I'm mistaken, doesn't even have 6 elements! Since the full line represents multiplication with the generator b and b^-1 = b. So it can't be isomorphic to any of the other ones.
I'm not really sure about my results. If you want, I can provide more details.
Thanks in advance for a glance.