*Originating author is Nitsa Movshovitz-Hadar.*

**Prolog**

This article is an English translation with emendations of a Hebrew paper written in 2014 about two years after the untimely passing of the illustrious lecturer and group theory expert, Professor David Chillag. It is dedicated to commemorating him. He entrusted me with the transparencies that accompanied his lecture on the enormous theorem presented in 2011 at the Technion Mathematical Club, hoping to produce a paper for teachers and teachers’ teachers on the subject. Unfortunately, we did not manage to do it together.

I thank those of our mutual colleagues who helped me with this, and at the same time, of course, I take full responsibility for things that are not entirely clear or even incorrect.

Nitsa Movshovitz-Hadar

### **Introduction – What is this article all about?**

The definition of a group in mathematics is an abstraction of the set of integers with the familiar operation of addition. A group is a set (such as the integers) with a binary operation which enables combining any two elements in the set and get as a result one element in the set (such as the sum of two integers), that has a few simple properties such as the existence of a unique “neutral element” (zero in the case of the integers). There is a large wealth of mathematical groups, differing from one another in composition and size. Some of them consist of a finite set (such as the set ), others consist of an infinite one (such as the integers). The binary operations vary as well (think, for example, about addition-modulo- defined on the finite set mentioned earlier, or about addition defined on the integers). The wealth of mathematical groups is so large that there is no chance of classifying even the finite ones of them. Fortunately, there is a special family of finite groups called *simple finite groups*, which *can *be classified. It turns out that this special family of finite groups is of great importance because, in some sense, *all* finite groups can be built from *simple* finite groups in a way that is somewhat analogous to the fact that all the positive integers can be built from the prime ones. The “enormous theorem,” the subject of this article, gives a complete classification of the simple finite groups. In this way, it provides tools for analyzing the structure and features of *all* finite groups. The theorem received its “enormous” nickname for some very good reason, to be explained below.

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