Group Actions | Keith Conrad
kconrad.math.uconn.edu · 11,412 words · saved by 1 readers
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GROUP ACTIONS KEITH CONRAD 1. Introduction The symmetric group Sn behaves, by its very definition, as permutations of the set {1, 2, . . . , n}. Dihedral groups Dn for n ≥ 3, while interpreted geometrically as certain mo- tions of the plane preserving a regular n-gon, can be considered as a group of permutations just of the n vertices; rigid motions of the vertices determine where the rest of the n-gon goes. If we label the n vertices in a definite manner by the numbers from 1 to n then we can view Dn…
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