Adjunction of roots to unitriangular groups over prime finite fields

In this paper we study embeddings of unitriangular groups UT${}_n({\mathbb{F}}_p)$ arising under adjunction of roots. We construct embeddings of UT${}_n({\mathbb{F}}_p)$ in UT${}_m({\mathbb{F}}_p)$, for $n\ge 2$, $m=(n-1)p^s + 1$,$s \in $\mathbb{Z}$^+$,suchthatanyelementofUT$_n($\mathbb{F}$_p)$hasa$p^s$-throotinUT$_m($\mathbb{F}$_p)$. Also we construct an embedding of the wreath product UT${}_n({\mathbb{F}}_p)\wr C_{p^s}$ in UT${}_m({\mathbb{F}}_p)$, where $C_{p^s}$ is the cyclic group of order $p^s$.