Singapore Haze & Subgroup of Smallest Prime Index

Recently, the Singapore Haze is getting quite bad, crossing the 200 PSI Mark on several occasions. Do consider purchasing a Air Purifier, or some N95 Masks, as the haze problem is probably staying for at least a month. Personally, I use Nasal Irrigation (Neilmed Sinus Rinse), which has tremendously helped my nose during this haze period. It can help clear out dust and mucus trapped in the nose.

Previously, we proved that any subgroup of index 2 is normal. It turns out that there is a generalisation of this theorem. Let $latex p$ be the smallest prime divisor of a group $latex G$. Then, any subgroup $latex Hleq…