A note on the automorphism group of the Hamming graph

Let m>1 be an integer and Ω be an m-set. The Hamming graph H(n,m) has Ωn as its vertex-set, with two vertices are adjacent if and only if they differ in exactly one coordinate. In this paper, we provide a new proof on the automorphism group of the Hamming graph H(n,m). Although our result is not new (CE Praeger, C Schneider, Permutation groups and Cartesian decompositions, Cambridge University Press, 2018), we believe that our proof is shorter and more elementary than the known proofs for determining the automorphism group of Hamming graph