Date of Graduation
Master of Science in Mathematics
group, subgroup, cyclic, nilpotent, abelian, involutions
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.
© James Alexander Cayley
Cayley, James Alexander, "Finite Groups in Which the Number of Cyclic Subgroups is 3/4 the Order of the Group" (2021). MSU Graduate Theses. 3695.