It's easy to show that $G$ is abelian if $a^2=e.$
Can't seem to figure out how to prove/disprove this.
2026-03-26 20:41:10.1774557670
In a group $G$, if $a^3=e$ for all $a$ belongs to $G$, then is $G$ abelian?
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The standard counterexample is the group of matrices of the form $$\pmatrix{1&a&b\\0&1&c\\0&0&1}$$ over the field of three elements.