Homotopical combinatorics uses tools from combinatorics to explore and understand structures in equivariant homotopy theory. One object of study in homotopical combinatorics is a G-transfer system, which is defined by five axioms. In this talk, we define transfer systems, and we present the difference between abelian transfer systems, where the order of operation on group elements doesn't matter, and nonabelian transfer systems, where order does matter. We describe how to find transfer system for cyclic groups, and contrast this with transfer systems for dihedral groups, which are nonabelian.
