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.

The people from the airlines were somewhat bored with their lives, strangely enough, and at night they would often go to bars to drink. I liked them all, and in order to be sociable, I would go with them to the bar to have a few drinks, several nights a week.

One day, about 3:30 in the afternoon, I was walking along the sidewalk opposite the beach at Copacabana past a bar. I suddenly got this treMENdous, strong feeling: "That's just what I want; that'll fit just right. I'd just love to have a drink right now!"

I started to walk into the bar, and I suddenly thought to myself, "Wait a minute! It's the middle of the afternoon. There's nobody here, There's no social reason to drink. Why do you have such a terribly strong feeling that you have to have a drink?" - and I got scared.

I never drank ever again, since then. I suppose I really wasn't in any danger, because I found it very easy to stop. But that strong feeling that I didn't understand frightened me. You see, I get such fun out of thinking that I don't want to destroy this most pleasant machine that makes life such a big kick. It's the same reason that, later on, I was reluctant to try experiments with LSD in spite of my curiosity about hallucinations.