# of elements of non-cyclic abelian groups

[kiddopop]

(a) Does there exist a non-cyclic abelian group having 66 elements? If so, give an example. If not, explain.
(b) Does there exist a non-cyclic abelian group having 99 elements? If so, give an example. If not, explain

 

[daon]

I would take a gander at the fundamental theorem of finite abelian groups. Use the fact that Zn + Zm is not cyclic if gcd(m,n) > 1