Show that any finite nilpotent group of square free order is cyclic.

Show that any finite nilpotent group of square free order is cyclic.

Hint: Suppose G is such a group. Any Sylow subgroup of G is of prime order.

Hint: Any finite nilpotent group is the direct product of its Sylow subgroups.

Hint: Use the Chinese Remainder Theorem.

Any idea,

• Ii think those hints are aplenty. Just mimick the proof of $C_3\times C_5\simeq C_{15}$. – Jyrki Lahtonen Dec 24 '18 at 4:45
• Also, I recommend that you take a look at our guide for new askers. – Jyrki Lahtonen Dec 24 '18 at 4:46