Classification of Finite Simple Groups

Classification Of Finite Simple Groups

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic building blocks of the natural numbers. The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups.

The proof of the theorem consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004. Gorenstein (d.1992), Lyons, and Solomon are gradually publishing a simplified and revised version of the proof.

Read more about Classification Of Finite Simple Groups:  Statement of The Classification Theorem, Overview of The Proof of The Classification Theorem, Second-generation Classification

Famous quotes containing the words finite, simple and/or groups:

    For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.
    Ralph Waldo Emerson (1803–1882)

    His pain was too great. He begged me for the simple mercy of death. And I could do nothing else but help him leave a world that had become a sleepless, tortured nightmare to him.
    Robert D. Andrews, and Nick Grindé. Dr. John Garth (Boris Karloff)

    Belonging to a group can provide the child with a variety of resources that an individual friendship often cannot—a sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social life—of inclusion and exclusion, conformity and independence.
    Zick Rubin (20th century)