Paper 2, Section I, 2G2 G

Groups, Rings and Modules
Part IB, 2012

What does it mean to say that the finite group GG acts on the set Ω\Omega ?

By considering an action of the symmetry group of a regular tetrahedron on a set of pairs of edges, show there is a surjective homomorphism S4S3S_{4} \rightarrow S_{3}.

[You may assume that the symmetric group SnS_{n} is generated by transpositions.]