Gamma-1-2 group

Symbol-free definition
A group is said to be a $$\Gamma_1^{(2)}$$ group if every element of the group belongs to a pair of mates of which at least one element is an involution (viz has order two).

Stronger properties

 * Suzuki group
 * Simple Chevalley group over a finite field of odd order

Weaker properties

 * 2-generated group
 * Finitely generated group