I need a help with determining if this statement is true or not.
Does every infinite group has infinite cyclic subgroup?
[Math] Does every infinite group has infinite cyclic subgroup
group-theoryinfinite-groups
group-theoryinfinite-groups
I need a help with determining if this statement is true or not.
Does every infinite group has infinite cyclic subgroup?
Best Answer
No. Just take $\mathbb{Z}_2\oplus \mathbb{Z}_2\oplus \mathbb{Z}_2 \oplus \ldots$.
Every element has finite order, so cannot generate an infinite group.