Classifying Primitive Groups using Computer Algebra and Change-Making

Abstract: Consider a primitive, solvable permutation group G acting on a set of elements X. Let G0 be the stabilizer of some element of X. Then the rank of G is the number of orbits of G0 acting on X. At an REU in Texas State University this past summer, I and three other students classified the groups of rank 5 and 6 and have described a potential way to classify groups of rank up to 200. In this presentation, I will introduce the basic group theory behind this problem, a surprising connection to change-making, the complexity of central problems in group theory, and the use of computer algebra systems.