Symmetry groups of Rosenbloom–Tsfasman spaces

Let Fqm⋅n be the vector space of m⋅nm⋅n-tuples over a finite field FqFq and P={1,2,…,m⋅n}P={1,2,…,m⋅n} a poset that is the finite union of mm disjoint chains of length nn. We consider on Fqm⋅n the poset-metric dPdP introduced by Rosenbloom and Tsfasman. In this paper, we give a complete description of the symmetry group of the metric space (V,dP)(V,dP).