nLab pariah group

Idea

The pariah groups (Griess 82) constitute the finite set of those 6 sporadic finite simple groups, which are not subquotients of the monster group, in contrast to the remaining 20 sporadic groups that constitute the Happy Family.

The pariah groups are: J1?, J3?, J4? (three of the four Janko groups), Ru? (the Rudvalis group), ON? (the O’Nan, or O’Nan–Sims, group), Ly? (the Lyons group). Coincidentally, $J_1$ and $J_4$ were the first and last sporadic groups discovered (after the five Mathieu groups in the 19th century).

References

• Robert Griess, Jr. The Friendly Giant, Invent. Math. 69 (1982) 1-102 (doi:10.1007/BF01389186)

See also

• Wikipedia, Pariah group