Generalized dihedral groups are strongly ambivalent

Statement
Let $$H$$ be an abelian group and $$G$$ be the fact about::generalized dihedral group corresponding to $$H$$. Then, $$G$$ is a fact about::strongly ambivalent group: every element of $$G$$ is a fact about::strongly real element. In other words, every element is either the identity element, or an involution, or the product of two involutions.

Related facts

 * Classification of rational generalized dihedral groups
 * Generalized dihedral groups are ambivalent
 * Symmetric groups are strongly ambivalent
 * Symmetric groups are rational