Class Year

2015

Date

4-22-2015

Document Type

Thesis

Distinguished Thesis

yes

Degree Name

Bachelor of Arts (BA)

Department or Program

Mathematics

First Advisor

David Yuen

Second Advisor

Enrique Treviño

Third Advisor

Michael Kash

Abstract

The fundamental theorem of finitely generated abelian groups describes precisely what its name suggests, a fundamental structure underlying finitely generated abelian groups. As such, it is an important result in group theory, but is considered too complex for the college-level Modern Algebra courses taught at Lake Forest College. I recall wanting a proof when I took the class, but one was not available at our current level, and so I have constructed a proof restricted almost exclusively to concepts encountered in Modern Algebra I. Furthermore, an application to the generation of finite fields and cryptography is presented, as a demonstration of the theorem’s utility.


Included in

Algebra Commons

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