Because every finite group is made up of "composition factors"—building blocks that are finite simple groups theorems about simple groups have ramifications for all finite groups.
Over the next ten years 26 new simple groups were found.
The challenge for mathematicians became how to classify the complete set of these simple groups.
Thompson's revolutionary ideas inspired and permeated an effort, hitherto considered hopeless, to determine all the finite simple groups.
In the late 1950s he began formulating a method for classifying finite simple groups, a task that absorbed his attention for the rest of his life.
Much as every integer can be broken down into a product of prime numbers, the symmetries of any object can be constructed from a collection of basic building blocks known as simple groups.
Finite groups and finitely presented simple groups are isolated.
Are there finitely generated simple groups of intermediate growth?
Figure 13 Comparison among the fundamental diagrams of experiments not including simple groups and including a set of simple groups of variable size.
Note that our results depend on Thompson's classification of the minimal simple groups and do not depend on the classification of finite simple groups.
Figure 12 Density profile for simulations in the T-junction scenario without simple groups (a) and in presence of simple groups (b).
