Abelianization of ambivalent group is elementary abelian 2-group

Statement

Suppose $G$ is an Ambivalent group (?). Then, the Abelianization (?) of $G$ is an Elementary abelian 2-group (?): it has exponent one or two.

Related facts

• Center of ambivalent group is elementary abelian 2-group
• Abelian and ambivalent iff elementary abelian 2-group
• Odd-order and ambivalent implies trivial

Facts used

1. Ambivalence is quotient-closed
2. Abelian and ambivalent iff elementary abelian 2-group

Proof

The proof follows directly from facts (1) and (2).