Let $A = \{1, 2, 3, 4\}$. What is the number of binary operations $*$ defined on $A$, such that $(A,*)$ is a group isomorphism to $(\Bbb Z_4,+)$, and the order of $3$ is $2$ in this group ?
I tried solving this using Cayley Tables but I am not really sure how to count all of them. All I know is that the structures of the tables should be similar in an isomorphism.
Can you explain how to do this?
I struggle with group theory so I would appreciate more "elementary" answers or at least detailed.
Thanks in advance !