Adjunction of roots to unitriangular groups over prime finite fields

Abstract

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 $n\ge 2$, $m=(n-1)p^s+1$, $s\in {\mathbb{Z}}^{+}$, such that any element of UT${}_n({\mathbb{F}}_p)$ has a $p^s$-th root in UT${}_m({\mathbb{F}}_p)$. 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 $p^s$.

15 pages

Cited by in corpus (1)

• $p$-solvability of regular equations over unitriangular groups over prime finite fields