Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

Paper 2, Section I, F

Groups, Rings and Modules | Part IB, 2011

Show that the quaternion group Q8={±1,±i,±j,±k}Q_{8}=\{\pm 1, \pm i, \pm j, \pm k\}Q8​={±1,±i,±j,±k}, with ij=k=−jii j=k=-j iij=k=−ji, i2=j2=k2=−1i^{2}=j^{2}=k^{2}=-1i2=j2=k2=−1, is not isomorphic to the symmetry group D8D_{8}D8​ of the square.

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