Definition: A group $G$ is said to be divisible if for any nonzero integer $n$ and for any $g \in G$ there exists $h \in G$ such that $g = h^n$.
Let $U_n(k)$ be the subgroup of unitriangular $n \times n$ matrices (upper triangular and all diagonal entries are $1$) with entries over a field $k$ with characteristic $0$, where $n \geq2$
Is $U_n(k)$ divisible? (it is true for $n = 2, 3$ if my computations are correct)
Thank you in advance.