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On The Number Of Distinct Cyclic Subgroups Of A Given Finite Group, Joseph Dillstrom
On The Number Of Distinct Cyclic Subgroups Of A Given Finite Group, Joseph Dillstrom
MSU Graduate Theses
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.