Foundations of finite group theory for a (future) computer

with a curious proposal. You, a ‘dynamic AI system’, were soon to be launched, and to demonstrate your capability to discover new mathematics with a mini-mum of instruction, they wanted a beginner’s course in elementary group theory (meant for a computer, of course). You were going to absorb the material and immediately start doing research. They claim that your capacity to comprehend written English, and familiar-ity with basic mathematics, is that of a good second year undergraduate. But your ability to assimilate and compute is astounding. After all, you trounced Deep Blue ten minutes after learning the rules for chess. GenghisV, one of the main gurus on the project, explained what was re-quired. “This beauty is a whiz. Give her the main definitions, I/O specifications, and general directions—then we’ll let’er rip. Getting her to do human mathematics is not so much the point, since GAP and MAGMA already do that very well. Mathematics by a computer for a computer is the goal here.