Date of Graduation

Fall 2021

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Richard Belshoff
Les Reid

Keywords

group, subgroup, cyclic, nilpotent, abelian, involutions

Subject Categories

Algebra

Abstract

Let $G$ be a finite group, c(G) denotes the number of cyclic subgroups of G and α(G) = c(G)/|G|. In this thesis we go over some basic properties of alpha, calculate alpha for some families of groups, with an emphasis on groups with α(G) = 3/4, as all groups with α(G) > 3/4 have been classified by Garonzi and Lima (2018). We find all Dihedral group with this property, show all groups with α(G) = 3/4 have at least |G|/2-1 involutions, and discuss existing work by Wall (1970) and Miller (1919) classifying all such groups.

Copyright

© James Alexander Cayley

Open Access

Included in

Algebra Commons

Share

COinS