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Abstract Algebra**Definition of Dihedral Group**

The ** dihedral group** is the group of symmetries of a regular polygon. In abstract algebra, it's a classic example of a finite, nonabelian group. Dihedral groups are also a great example of how

**Example of a Dihedral Group**

This group is easy to work with computationally, and provides a great example of a connection between groups and geometry. For example, imagine an equilateral triangle. There are a total of 6 different transformations (try to imagine what they are.) And it's nonabelian because a flip-then-rotate is not the same as a rotate-then flip. It's good practice to make a list of all the transformations, and determine which one is the identity element, and check that every transformation has an *inverse*.

**Consider this...**

The *dihedral groups* give you groups that act on geometry. Is there any way to use our knowledge of regular polygons to help us study these groups?

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Course Description

Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.