nLab Happy Family



Exceptional structures

Group Theory



What has been called the Happy Family in Griess 82 is the finite set of those 20 of the 26 sporadic finite simple groups, which are subquotients of the monster group, in contrast to the remaining 6 pariah groups.

The Happy Family is taken to be formed of three generations:

It has been suggested (Lentner 12) that these three generations are generated by an iterated process of forming the centralizer of an involution of a simple group, starting out from the simple group of Lie-type SL 3(4)SL_3(4).


See also

Last revised on February 24, 2021 at 18:23:02. See the history of this page for a list of all contributions to it.