Q: A group without proper subgroups is a cyclic group If a group $G$ has no nontrival proper subgroups, prove that $G$ is a cyclic group with order $p$, where $p$ is a prime number.

A: Hint :
For some non identity element $g\in G$ what can you say about group generated by $g$.. 


*

*Can $\langle g\rangle$ be a proper subgroup?

