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In group theory, the quaternion group Q8 is a non-abelian group of order eight, isomorphic to the eight-element subset { 1 , i , j , k , − 1 , − i , − j , − k } {\displaystyle \{1,i,j,k,-1,-i,-j,-k\}} of the quaternions under multiplication. It is given by the group presentation
where e is the identity element and e commutes with the other elements of the group.
Another presentation of Q8 is
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