Pariah group

Diagram of sporadic simple groups, showing the pariahs as 4 groups on the right, and 2 groups as extensions of Happy Family groups.

In mathematical group theory, the term pariah was introduced by Griess (1982) to refer to the six sporadic simple groups that are not subquotients of the monster group.

These groups are:

• Three of the Janko groups: J₁, J₃, and J₄.
• The Lyons group (Ly)
• The O'Nan group
• The Rudvalis group

References

• Greiss, Robert L. (1982), "The friendly giant", Inventiones Mathematicae 69 (1): 1–102, doi:10.1007/BF01389186, ISSN 0020-9910, MR 671653