Editing Monster group (section)

==History==
The monster was predicted by [[Bernd Fischer (mathematician)|Bernd Fischer]] (unpublished, about 1973) and [[Robert Griess]]{{sfn|Griess|1976|pp=113–118}} as a simple group containing a [[Double covering group|double cover]] of Fischer's [[baby monster group]] as a [[Centralizer and normalizer|centralizer]] of an [[Involution (group theory)|involution]].  Within a few months, the order of M was found by Griess using the [[Thompson order formula]], and Fischer,  [[John Horton Conway|Conway]], Norton and Thompson discovered other groups as subquotients, including many of the known sporadic groups, and two new ones: the [[Thompson group (finite)|Thompson group]] and the [[Harada–Norton group]]. The [[Character theory|character table]] of the monster, a 194-by-194 array, was calculated in 1979 by Fischer and Donald Livingstone using computer programs written by Michael Thorne. It was not clear in the 1970s whether the monster actually existed. Griess{{sfn|Griess|1982|pp=1–102}} constructed M as the [[automorphism group]] of the [[Griess algebra]], a 196,883-dimensional commutative [[nonassociative algebra]] over the real numbers; he first announced his construction in [[Ann Arbor]] on January 14, 1980. In his 1982 paper, he referred to the monster as the Friendly Giant, but this name has not been generally adopted. [[John Horton Conway|John Conway]]{{sfn|Conway|1985|pp=513–540}} and [[Jacques Tits]]{{sfn|Tits|1983|pp=105–122}}{{sfn|Tits|1984|pp=491–499}} subsequently simplified this construction.

Griess's construction showed that the monster exists. [[John G. Thompson|Thompson]]{{sfn|Thompson|1979|pp=340–346}} showed that its uniqueness (as a simple group satisfying certain conditions coming from the classification of finite simple groups) would follow from the existence of a 196,883-dimensional [[faithful representation]]. A proof of the existence of such a representation was announced by [[Simon P. Norton|Norton]],{{sfn|Norton|1985|pp=271–285}} though he never published the details. Griess, Meierfrankenfeld, and Segev gave the first complete published proof of the uniqueness of the monster (more precisely, they showed that a group with the same centralizers of involutions as the monster is isomorphic to the monster).{{sfn|Griess|Meierfrankenfeld|Segev|1989|pp=567–602}}

The monster was a culmination of the development of sporadic simple groups and can be built from any two of three subquotients: the [[Fischer group]] Fi<sub>24</sub>, the baby monster, and the [[Conway group]] Co<sub>1</sub>.

The [[Schur multiplier]] and the [[outer automorphism group]] of the monster are both [[Trivial group|trivial]].