Ciro Santilli @cirosantilli 37

Given G and a normal subgroup N, then G is a group extension of G/N by N. One could ask whether this extension is trivial or split; in other words, one could ask whether G is a direct product or semidirect product of N and G/N. This is a special case of the extension problem. An example where the extension is not split is as follows: Let $G=Z4=0,1,2,3$, and $=0,2$ which is isomorphic to Z2. Then G/N is also isomorphic to Z2. But Z2 has only the trivial automorphism, so the only semi-direct product of N and G/N is the direct product. Since Z4 is different from Z2 × Z2, we conclude that G is not a semi-direct product of N and G/N.

A while ago a Singaporean taxi driver asked me what a UK hawker centre lunch might cost. I explained that there aren't any. He asked what office workers ate, and I explained the concept of Meal deals. And he looked at me with such a powerful combination of pity and revulsion.

The way to get a woman is not to have money, not to look nice, not to have a nice personality. The way to get a woman, is to always be available, night or day. Any time you phone, you're there, or you're at the bar. They know that you are available at all times. It is very, very important to a woman.