Date of Graduation
Master of Science in Mathematics
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.
subgroup lattice, chromatic number, supersolvable, projective special linear groups, lattice, Hasse diagram
© Jacob C. Miles
Miles, Jacob C., "On the Chromatic Numbers of Subgroup Lattices" (2022). MSU Graduate Theses. 3751.