Contemporary Abstract Algebra

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Presentation transcript:

Contemporary Abstract Algebra SEVENTH EDITION Joseph A. Gallian

Chapter 1: Introduction to Groups Symmetries of a Square The Dihedral Groups

1.1 Symmetries of a Square

The Square 1/3

The Square 2/3

The Square 3/3

Multiplication

The Dihedral Group The analysis carried out above for a square can similarly be done for an equilateral triangle or regular pentagon or, indeed, any regular n-gon (n ≥ 3). The corresponding group is denoted by and is called the dihedral group of order 2n.

The Dihedral Group This group has 2n elements n rotations, namely n reflection: Example: