On the representation of groups approximated by finite p-groups

We present faithful triangular representations of finite Kaluzhnin p-groups Pp,n over the field of p elements. This enables us to obtain a triangular representation of the projective limit Pp for the groups Pp,n. The obtained representation is studied by using the language of matrix templates specially developed for this purpose. As an example, we present a triangular representation of the well-known self-similar Gupta–Sidki 3-group.