Video: How to Make a Cayley Table

Video Summary for Cayley Tables

This video explains how to construct and understand Cayley tables for finite groups.

A Cayley table is essentially a multiplication table that shows the relationships between elements in a group under a specific operation.

The video demonstrates how to build a Cayley table using examples like the cyclic group of order 3 and the symmetries of an equilateral triangle.

Key properties of Cayley tables include:

• Each row and column must contain each group element exactly once
• The identity element row and column match the headings
• Every entry must be an element of the group

Creating a Cayley table involves listing all group elements along the top row and left column, then filling in each cell by applying the group operation.

Once completed, a Cayley table serves as a "dictionary" for understanding the structure of a group and its operations.