Subgroup of Index Least Prime Divisor is Normal

Theorem

Let $G$ be a finite group of order $n>1$.

Let $p$ be the least prime divisor of $n$.

Let $H$ be a subgroup of index $p$.

Then $H$ is normal.

Proof

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Also see

• Subgroup of Index 2 is Normal