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.

[S$89.90][Clean Air]2015 Air Purifier Singapore brand and 1 year warranty with HEPA Activated Carbon UV-C germicidal killer lamp silent operation and high efficiency etc

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[S$19.90]Haze Prevention~ Nasal Rinse™- Flush out mucous~germs~bacteria~and dirt internally. Clear blocked nose and very soothing.

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

Proof: Let be a subgroup of of index . Let act on the left cosets of by left multiplication: , .

This group action induces a group homomorphism .

Let . If , then for all . In particular when g=1, xH=H, i.e. .

Thus . In particular, , since is a normal subgroup of .

We have . Thus .

Also note that . Note that since .

Let be a prime divisor of . Then since . Also, . Since is the smallest prime divisor of , . Therefore, , i.e. .

Then , i.e. H=K. Thus, H is normal in G.

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I’m shocked to hear how bad the haze has gotten.

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Yeah, it is pretty bad, my lungs hurt after breathing in the air.

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