#### 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

#### Recommended Citation

Dillstrom, Joseph, "On The Number Of Distinct Cyclic Subgroups Of A Given Finite Group" (2016). *MSU Graduate Theses*. 2547.

https://bearworks.missouristate.edu/theses/2547