Abelianization of ambivalent group is elementary abelian 2-group

Statement
Suppose $$G$$ is an fact about::ambivalent group. Then, the fact about::abelianization of $$G$$ is an fact about::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) uses::Ambivalence is quotient-closed
 * 2) uses::Abelian and ambivalent iff elementary abelian 2-group

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