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Contemporary Abstract Algebra

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 S quare 3/3. Multiplication. The Dihedral Group.

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Contemporary Abstract Algebra

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  1. Contemporary Abstract Algebra SEVENTH EDITION Joseph A. Gallian

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

  3. 1.1 Symmetries of a Square

  4. The Square 1/3

  5. The Square 2/3

  6. The Square 3/3

  7. Multiplication

  8. 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.

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

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