High Quality Content by WIKIPEDIA articles! In group theory, the quaternion group is a non-abelian group of order 8, isomorphic to a certain eight-element subset of the quaternions under multiplication. It is often denoted by Q or Q8, and is given by the group presentation Q = langle -1,i,j,k mid (-1)^2 = 1, ;i^2 = j^2 = k^2 = ijk = -1 rangle, ,! where 1 is the identity element and ?1 commutes with the other elements of the group.

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