Pariah

This article is about a term related to the Classification of finite simple groups

This article defines a group property that can be evaluated, or makes sense, for simple groups

Definition

Implicit definition

A pariah is a sporadic simple group that does not occur as a subquotient of the Monster group.

Explicit definition

The following are the pariahs:

• Three of the Janko groups viz $J_{1}$, $J_{3}$ and $J_{4}$
• The O'Nan group
• The Rudvalis group
• The Lyons group