Paper 3, Section II, D

Groups | Part IA, 2010

(i) State the orbit-stabilizer theorem.

Let GG be the group of rotations of the cube, XX the set of faces. Identify the stabilizer of a face, and hence compute the order of GG.

Describe the orbits of GG on the set X×XX \times X of pairs of faces.

(ii) Define what it means for a subgroup NN of GG to be normal. Show that GG has a normal subgroup of order 4 .

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