The quaternion group has the following presentation: \begin{eqnarray} Q=\langle i,j,k|ijk^{-1},ik^{-1}j^{-1},ij^{-1}k\rangle. \end{eqnarray} I have derived down $i^2=j^2=k^2$ by a proper multiplication of the words in the relation. My question is how to get $i^4=j^4=k^4=1$.
2026-03-26 04:51:45.1774500705
Presentation of the quaternion group
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