Bachelor of Arts (BA)
Department or Program
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.
Pepper, Turner J., "Structure of Finitely Generated Abelian Groups" (2015). Senior Theses.