# Math Help - group

1. ## group

Let G be a group with $|G|=30$ .Prove that G is izomorf with the group of 30-th roots of unity .

2. ## Not true

If a group has order 30 there are 4 unique groups (up to isomorphism) to which it could be isomorphic.
Abelian
1) $\mathbb{Z}_{30}$ this is the one you are looking for
Nonabelian
2) $D_{15}$ (Dihedral group)
3) $D_5 \times Z_3$
4) $D_3 \times Z_5$

If its abelian its easy to see why it must be cyclic by the fundamental theorem of finitely generated abelian groups, and noting $30=2*3*5$

hope this helps