Question

Give an example of three different groups with eight elements. why are the groups different?

Answer 1

Three groups with eight elements are: the cyclic group of order 8, the dihedral group of order 8, and the direct product of three cyclic groups of order two. The first group is the only group among the three that contains any elements of order 8. The second group is the only nonabelian group among the three. The third group is the only group in which every nonidentity element has order 2.