Abstract
For a finite group G, a positive integer λ, and subsets X,Y of G, write λG=XY if the products xy (x∈X,y∈Y), cover G precisely λ times. Such a subset Y is called a code with respect to X, and when λ=1 it is a perfect code in the Cayley graph Cay (G, X). In this paper we present various families of examples of such codes, with X closed under conjugation and Y a subgroup, in symmetric groups, and also in special linear groups SL2(q). We also propose conjectures about the existence of some much wider families.
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