On the representation of groups approximated by finite p-groups

Abstract

Faithful triangular representations of finite Kaloujnine $p$-groups are presented. This allows us to obtain a triangular representation of the projective limit $P_p$ of groups $P_{p,n}$. The obtained representation is studied by using a 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.