Date of Graduation

Spring 2016

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Richard Belshoff

Keywords

abstract algebra, group theory, finite group, cyclic subgroup, Lagrange's Theorem

Subject Categories

Mathematics

Abstract

In the study of finite groups, it is a natural question to consider the number of distinct cyclic subgroups of a given finite group. Following an article by M. Tarnauceanu in the American Mathematical Monthly, we consider arithmetic relations between the order of a finite group and the number of its cyclic subgroups. We classify several infinite families of finite groups in this fashion and expand upon an open problem posed in the article.

Copyright

© Joseph Dillstrom

Open Access

Included in

Mathematics Commons

Share

COinS