# Abelianization of ambivalent group is elementary abelian 2-group

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## Contents

## Statement

Suppose is an Ambivalent group (?). Then, the Abelianization (?) of 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

## Proof

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