If $G$ has only 2 non-trivial proper subgroups H, N
, then H, N are cyclic subgroup of $G$.
I searched essentially same problem at
So, I already know the solving method of my question.
- $G$ is cyclic.
- subgroup of cyclic subgroup is cyclic.
- Therefore H, N are cyclic.
$$ $$ In this time,
I'd like to know other method solving my question.
Can anybody show my question, not through "$G$ is cyclic."
Umm, maybe this is useless question.... :-(
But I spent lots of time for solving this question.
Thank you for your attention to this matter.