About 1981 the finite group theory community decided via some sort of collective decision that the following result had been proved: Classification Theorem Each finite simple group is isomorphic to one of the following: (1) A group of prime order. (2) An alternating group. (3) A group of Lie type. (4) One of 26 sporadic groups. There are many things to be said about this theorem and eventually I'll get around to saying some of them. But for the moment I'll only pose a few questions to give you some things to think about: Question 1. What is a simple group and why are simple groups interesting? Question 2. What are the families of groups appearing in the conclusion of the Classification? In particular what is involved in describing these families and how useful is the description?
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