Ambivalence is direct product-closed

This article gives the statement, and possibly proof, of a group property (i.e., ambivalent group) satisfying a group metaproperty (i.e., direct product-closed group property)
View all group metaproperty satisfactions | View all group metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for group properties
Get more facts about ambivalent group |Get facts that use property satisfaction of ambivalent group | Get facts that use property satisfaction of ambivalent group|Get more facts about direct product-closed group property

Statement

Statement with symbols

Suppose $I$ is an indexing set and $G_i, i \in I$, is a collection of ambivalent groups. Let $G$ be the external direct product of the $G_i$s. Then, $G$ is also an ambivalent group.

Related facts

• Every element is automorphic to its inverse is direct product-closed
• Conjugacy-closed subgroup of ambivalent group is ambivalent