Visual Group Theory, Lecture 2.3: Symmetric and alternating groups
Автор: Professor Macauley
Загружено: 2016-02-27
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Visual Group Theory, Lecture 2.3: Symmetric and alternating groups
In this lecture, we introduce the last two of our "5 families" of groups: (4) symmetric groups and (5) alternating groups. The symmetric group S_n is the group of all n! permutations of {1,...,n}. We see several different ways to describe permutations, though we primarily stick with the "cycle notation". The alternating group A_n is a subgroup of S_n, and it consists of the permutations that can be written as a product of an even number of transpositions. There are exactly five regular three-dimensional convex polyhedra (tetrahedron, cube, octahedron, dodecahedron, icosahedron), and the symmetry groups of each of these are symmetric or alternating groups.
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