Mihran Papikian, Thesis Supervisor Sergei Tabachnikov, Thesis Honors Advisor
Keywords:
math linear algebra group theory abstract algebra
Abstract:
This thesis examines the relationship between the theory of finite abelian groups and the theory of linear operators over finite-dimensional vector spaces. We introduce the basic notions of module theory which allows us to generalize many facts about abelian groups and vector spaces. After stating several fundamental results from group theory, we proceed to prove that there exist analogous results in the study of finite-dimensional vector spaces. We also demonstrate that many of the fundamental objects of study in linear algebra, such as the minimal and characteristic polynomial, play the same role as some group-theoretic object.
