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The quaternion group is a non-abelian group of order eight: ${\displaystyle \mathrm {Q} _{8}=\langle {\bar {e}},i,j,k\mid {\bar {e}}^{2}=e,\;i^{2}=j^{2}=k^{2}=ijk={\bar {e}}\rangle ,}$ where $e$ is the identity element and ${\bar {e}}$ commutes with the other elements of the group.

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