Give example (if exists) of an infinite abelian group having a non-cyclic finite subgroup . Please help
2026-03-26 22:15:22.1774563322
Example of an infinite abelian group having a non-cyclic finite subgroup
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The simplest non-cyclic finite group is the Klein four-group $V = C_2 \times C_2$.
So,we can just take $\mathbb Z \times V$.
More generally, take any nontrivial finite abelian group $G$ and take $\mathbb Z \times G \times G$.