Conjugacy-closed subgroup of ambivalent group is ambivalent

Statement

Verbal statement

Any Conjugacy-closed subgroup (?) of an Ambivalent group (?) is an ambivalent group.

In particular, any Conjugacy-closed normal subgroup (?), Central factor (?), Retract (?), or Direct factor (?) of an ambivalent group is ambivalent.

Related facts

• Ambivalence is direct product-closed
• Normal subgroup of ambivalent group implies every element is automorphic to its inverse
• Every element is automorphic to its inverse is characteristic subgroup-closed