Paper 3, Section I, D

Groups | Part IA, 2011

(a) Let GG be the group of symmetries of the cube, and consider the action of GG on the set of edges of the cube. Determine the stabilizer of an edge and its orbit. Hence compute the order of GG.

(b) The symmetric group SnS_{n} acts on the set X={1,,n}X=\{1, \ldots, n\}, and hence acts on X×XX \times X by g(x,y)=(gx,gy)g(x, y)=(g x, g y). Determine the orbits of SnS_{n} on X×XX \times X.

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