Ciro Santilli @cirosantilli 40

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 earth moved," Maria said, not looking at Pilar. "Truly. It was a thing I cannot tell thee."

"It never moves more than three times in a lifetime. Did it really move?" Pilar Said.

"Yes," the girl said. "Truly."

"For you, Inglés?" Pilar looked at Robert Jordan. "Don't lie."

"Yes," he said. "Truly."