#### Thesis Title

On Proofs of Sylow's Theorem

#### Date of Graduation

Summer 2000

#### Degree

Master of Science in Mathematics

#### Department

Mathematics

#### Committee Chair

Kishor Shah

#### Subject Categories

Mathematics

#### Abstract

We give five proofs of Sylow's Theorem. The proofs given will be Sylow's original proof, the Cauchy-Frobenius proof using double cosets, Frobenius' proof (two versions) using the class equation, and Wielandt's proof using subsets. We give a number of different examples to illustrate the various proofs. We put Sylow's work in historical context. We give an application of Sylow's Theorem in the proof of the Fundamental Theorem of Algebra. We give a determination of conjugacy classes in the Dihedral group. We conclude with a sketch of Sylow.

#### Copyright

© Lucille Marshall

#### Recommended Citation

Marshall, Lucille, "On Proofs of Sylow's Theorem" (2000). *MSU Graduate Theses*. 854.

https://bearworks.missouristate.edu/theses/854

**Dissertation/Thesis**