Let p be a prime number and let G_p be the variety of all languages recognised by a finite p-group. We give a construction Let p be a prime number and let G_p be the variety of all languages recognised by a finite p-group. We give a construction process of all G_p preserving functions from a free monoid to a free group. Our result follows from a new noncommutative generalization of Mahler’s theorem on interpolation series, a celebrated result of p-adic analysis.