Date of Graduation
Master of Science in Mathematics
abstract algebra, group theory, finite group, cyclic subgroup, Lagrange's Theorem
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.
© Joseph Dillstrom
Dillstrom, Joseph, "On The Number Of Distinct Cyclic Subgroups Of A Given Finite Group" (2016). MSU Graduate Theses. 2547.