Groups, symmetries, Cayley tables and graphs | Group theory episode 2

#abstractalgebra #grouptheory

Groups are perfect for describing the symmetries of shapes and other objects. In this video, we look at many examples, including their Cayley tables and Cayley graphs. We explore the rotations and reflections of a square, and we discover a curious internal block structure. This will lead to a discussion about subgroups and quotient groups in upcoming videos.

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0:00 Introduction
1:08 Symmetries
3:49 Inverses
7:06 The rotations of a square
7:57 Cayley table
10:57 Isomorphic groups
13:42 Cayley graph
15:33 The reflections of a square
17:41 Orientation
20:18 Generators
23:18 Other polygons
24:46 What's next?

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