Properties
Symmetric groups are Coxeter groups and reflection groups. They can be realized as a group of reflections with respect to hyperplanes . Braid groups Bn admit symmetric groups Sn as quotient groups.
Cayley's theorem states that every group G is isomorphic to a subgroup of the symmetric group on the elements of G, as a group acts on itself faithfully by (left or right) multiplication.
Read more about this topic: Symmetric Group
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