Contents

group theory

# Contents

## Idea

The pariah groups (Griess 82) constitute the finite set of those 6 sporadic finite simple groups, which are not subquotients of 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).