Question

Example of finite abelian group which is not cyclic

Answer 1

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First, show that if a finite abelian group is not cyclic, then it contains a subgroup isomorphic to for some prime . Let be a finite abelian group. ... You can see contains a subgroup isomorphic for the same prime , because if all components in the direct product correspond to distinct primes, then would by cyclic.

Answer 2

It is noncyclic group but it's nay subgroup is cyclic ... Quaternion group is a non cyclic non abelian group in which each proper subgroup

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