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Finite Simple Groups

Date: 3/15/96 at 0:23:57
From: Anonymous
Subject: What is the Monster?

What is the Monster - large finite simple group - and why is it

Date: 3/24/96 at 15:51:23
From: Doctor Steven
Subject: Re: What is the Monster?

The classification of the finite simple groups has been basically 
what has driven the study of abstract algebra in the 20th century.

The finite simple groups are:

    Z_p where p is prime  - the integers modulo a prime.

    A_n where n > 5       - the alternating groups

    Lie algebras          - I don't understand these

    Sporadic Groups       - I don't understand these either,
                             either, but the Monster is in here

This classification was finished in the 1980's and covered over 
15,000 pages of proofs.  A serious effort, led by Daniel 
Gorenstein, is under way to condense this into a concise 3000-5000 
page proof.

The reason why the Monster is interesting is because it's the 
largest of the sporadic groups (hence the name), and several other 
sporadic groups can be determined by studying its structure.  Also 
interesting is that this group was investigated by hand, while 
most other sporadic groups were found using very large computers 
running for very long times.

Some more information can be gotten on the Monster, and finite 
simple groups in general, by reading this book:

  Mathematical Surveys and Monographs: The Classification of the 

  <i>Simple Groups</i> by Daniel Gorenstein, Lyons and Solomon,  
The American Mathematical Society, 1994.

Hope this helps.

-Doctor Steven,  The Math Forum

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