#### Date of Award

3-2014

#### Document Type

Thesis

#### Degree Name

Master of Arts in Mathematics

#### Department

Mathematics

#### First Reader/Committee Chair

Dr. Giovanna Llosent

#### Abstract

Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex numbers and if U is an invariant subspace of φ, then U has a complementary reducing subspace W .

The objective of this thesis is to find all irreducible representations of the dihedral group D2n. The reason we will work with the dihedral group is because it is one of the first and most intuitive non-abelian group we encounter in abstract algebra. I will compute the representations and characters of D2n and my thesis will be an explanation of these computations. When n = 2k + 1 we will show that there are k + 2 irreducible representations of D2n, but when n = 2k we will see that D2n has k + 3 irreducible rep- resentations. To achieve this we will first give some background in group, ring, module, and vector space theory that is used in representation theory. We will then explain what general representation theory is. Finally we will show how we arrived at our conclusion.

#### Recommended Citation

Soto, Melissa, "The Irreducible Representations of D2n" (2014). *Electronic Theses, Projects, and Dissertations*. 12.

http://scholarworks.lib.csusb.edu/etd/12