Strongly ambivalent group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

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

Relation with other properties

Weaker properties

• Ambivalent group
• Group having a class-inverting automorphism
• 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