Strongly ambivalent group

Definition
A group is termed a strongly ambivalent group if every element in the group is a defining ingredient::strongly real element: it is either the identity element, or an involution (element of order two) or the product of two involutions.

Weaker properties

 * Stronger than::Ambivalent group
 * Stronger than::Group having a class-inverting automorphism
 * Stronger than::Group in which every element is automorphic to its inverse

Facts

 * Symmetric groups are strongly ambivalent
 * Dihedral groups are strongly ambivalent
 * Generalized dihedral groups are strongly ambivalent