Date of Graduation
Spring 2021
Degree
Master of Natural and Applied Science in Mathematics
Department
Mathematics
Committee Chair
Les Reid
Abstract
In this paper we discuss the Hamiltonicity of the subgroup lattices of
different classes of groups. We provide sufficient conditions for the
Hamiltonicity of the subgroup lattices of cube-free abelian groups. We also
prove the non-Hamiltonicity of the subgroup lattices of dihedral and
dicyclic groups. We disprove a conjecture on non-abelian p-groups by
producing an infinite family of non-abelian p-groups with Hamiltonian
subgroup lattices. Finally, we provide a list of the Hamiltonicity of the
subgroup lattices of every finite group up to order 35 barring two groups.
Keywords
group theory, graph theory, Hamiltonian, subgroup lattice, group, graph, lattice
Subject Categories
Algebra | Discrete Mathematics and Combinatorics
Copyright
© Nicholas Charles Fleece
Recommended Citation
Fleece, Nicholas Charles, "On the Hamiltonicity of Subgroup Lattices" (2021). MSU Graduate Theses/Dissertations. 3605.
https://bearworks.missouristate.edu/theses/3605
