A group without proper subgroups is a cyclic group

Question

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.

Except if the group is trivial. – Marc van Leeuwen Apr 02 '14 at 07:09 — Marc van Leeuwen, Apr 02 '14 at 07:09

score 1 · Accepted Answer · answered Apr 02 '14 at 07:10

1

Hint :

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

answered Apr 02 '14 at 07:10

1 Answers1