Let G be a group with .Prove that G is izomorf with the group of 30-th roots of unity .
If a group has order 30 there are 4 unique groups (up to isomorphism) to which it could be isomorphic.
Abelian
1) this is the one you are looking for
Nonabelian
2) (Dihedral group)
3)
4)
If its abelian its easy to see why it must be cyclic by the fundamental theorem of finitely generated abelian groups, and noting
hope this helps