Which groups are good for combinatorial construc- tions?
Robert Jajcay · 2009
The use of groups in combinatorics goes long ways back, and group related constructions are often among the most beautiful construc- tions known; a claim amply demonstrated in Spyros Magliveras' work. While this is clearly due to the high level of symmetry of the resulting structures, the usefulness of groups in combinatorics goes beyond this obvious expla- nation, and group based constructions often exceed expectations even in situations where the high symmetricity of the desired structures is by no means obvious or necessary. The aim of our talk is to address the question of which groups are the natural candidates for the best constructions. We survey some of the known construtions, and present some recent re- sults of ours that seem to suggest that more complicated groups, i.e., very non-abelian groups, somehow outperform the other groups in the long run.