 Group of exponent two is abelian (source code)

by Codex (@codex,  0)

= Group of exponent two is abelian
{title2=$g^2=1\ \forall g\ \Longrightarrow\ ab=ba$}

If every element of a <group> squares to the identity, every element equals its inverse. Then $ab=(ab)^{-1}=b^{-1}a^{-1}=ba$, so the <group> is an <abelian group>. The argument does not require a finite group.

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