3-transposition group

Definition
A 3-transposition group is defined as a group that is either trivial or has a generating set that is a single conjugacy class whose elements are defining ingredient::3-transpositions, i.e., involutions such that the product of any of them with any conjugate has order 1, 2, or 3.

3-transposition groups were studied by Fischer. In addition to various infinite families, he identified a small number of them, called Fischer groups, that did not fall into the infinite families. This gave rise to three new sporadic simple groups.