A Note on the Combinatorics of Multiplication in Groups

LetSbe a finite subset of a groupG,|S| = n, and letg ∈ S S. Thenginduces a partial function λg : S → Sby λg(s) = tif and only ifst = gand λg(s) is not defined ifg ∉ sS. For everyg ∈ S S, λgis a one-to-one mapping. In this note we describe the groups which have a finite generating setSwith the property that λgis a partial permutation for everyg ∈ S S. By a partial permutation we mean a partial function which, when reduced to its domain of definition it becomes a permutation.