Date of Graduation

Spring 2021

Degree

Master of Natural and Applied Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

group theory, graph theory, Hamiltonian, subgroup lattice, group, graph, lattice

Subject Categories

Algebra | Discrete Mathematics and Combinatorics

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.

Copyright

© Nicholas Charles Fleece

Open Access

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