Date of Graduation
Spring 2022
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Les Reid
Abstract
In this thesis we investigate the chromatic number of the Hasse diagram of a subgroup lattice. We combine results of Bollobás and Tůma to show that there exist infnite groups whose subgroup lattices have arbitarily high chromatic numbers. We show that fnite supersolvable groups have bipartite subgroup lattices but that CLT and non-solvable groups may not have bipartite subgroup lattices. Lastly, we give a preliminary argument suggesting that there are an infnite number of non-solvable groups whose subgroup lattices are bipartite.
Keywords
subgroup lattice, chromatic number, supersolvable, projective special linear groups, lattice, Hasse diagram
Subject Categories
Algebra
Copyright
© Jacob C. Miles
Recommended Citation
Miles, Jacob C., "On the Chromatic Numbers of Subgroup Lattices" (2022). MSU Graduate Theses. 3751.
https://bearworks.missouristate.edu/theses/3751
