Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
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Paper 1, Section I, F

Geometry of Group Actions | Part II, 2010

Explain what it means to say that GGG is a crystallographic group of isometries of the Euclidean plane and that Gˉ\bar{G}Gˉ is its point group. Prove the crystallographic restriction: a rotation in such a point group Gˉ\bar{G}Gˉ must have order 1,2,3,41,2,3,41,2,3,4 or 6 .

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