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Full-Text Articles in Physical Sciences and Mathematics
On The Chromatic Numbers Of Subgroup Lattices, Jacob C. Miles
On The Chromatic Numbers Of Subgroup Lattices, Jacob C. Miles
MSU Graduate Theses
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.
Dot Product Bounds In Galois Rings, David Lee Crosby
Dot Product Bounds In Galois Rings, David Lee Crosby
MSU Graduate Theses
We consider the Erdős Distance Conjecture in the context of dot products in Galois rings and prove results for single dot products and pairs of dot products.