Encyclopedia > Monster group

  Article Content

Monster group

The Monster group M is a mathematical group of order
   246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71
= 808017424794512875886459904961710757005754368000000000
≈ 8 · 1053.
It is a simple group, meaning it does not have any normal subgroups except for the subgroup consisting only of the identity element, and M itself.

The finite simple groups have been completely classified; there are several infinite families of finite simple groups, plus a number of "sporadic groups" that don't follow any pattern. The Monster group is the largest of these sporadic groups. See classification of finite simple groups.

The Monster was found by B. Fischer and R. Griess in 1973. It can be constructed as a group of rotations in a space of dimension 196,883 over the rational numbers.

The Monster group prominently features in the Monstrous Moonshine conjecture[?] which relates discrete and non-discrete mathematics and was proven by Richard Borcherds[?] in 1989.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Photosynthesis

... to ferredoxin[?], then to plastoquinone[?] (a complex of two cytochromes similar to those found in mitochondria), and then plastocyanin[?] before returning t ...

 
 
 
This page was created in 34.9 ms