If $G$ has no proper subgroups other than the trivial group,then $G$ is a finite group. If $G$ has no proper subgroups other than the trivial group,then show that $G$ is a finite group.



totally stuck.can I get some help
Assume $G$ is infinite and $1\ne g\in G$. Then $\langle g\rangle$ is either a proper subgroup, or one has $G=\langle g\rangle\cong \mathbb Z$, which has the proper subgroup $2\mathbb Z$
See the subgroup generated by an element of $G$.