Term for a group where every element is its own inverse?

They are often called Boolean groups.


Another term for these groups is elementary abelian $2$-groups. In general, an elementary abelian $p$-group (for a prime $p$) is an abelian group where every non-identity element has order $p$ (and it is easy to see that if all non-identity elements have the same order, then that order must be a prime).


These are (the underlying additive groups of) the vector spaces over $\Bbb{Z}/2\Bbb{Z}$.

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Terminology

Abstract Algebra

Group Theory

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