Existence of isomorphism between groups of upper triangular matrices. Is there an isomorphism between this group of matrices
$$
\begin{pmatrix}
1 & k \\
0 & 1 \\
\end{pmatrix},~~k\in\mathbb Z
$$
and this one
$$
\begin{pmatrix}
1 & k_1 & k_2 \\
0 & 1   & k_3 \\
0 & 0   & 1
\end{pmatrix},~~k_1,k_2,k_3\in\mathbb Z
$$
?

The set of matrices of the form
$$
\begin{pmatrix}
1 & k \\
0 & 1 \\
\end{pmatrix},~~k\in\mathbb Z
$$
forms a cylic group under matrix multiplication (Find the generator).
How about the set of matrices of this form?
$$
\begin{pmatrix}
1 & k_1 & k_2 \\
0 & 1   & k_3 \\
0 & 0   & 1
\end{pmatrix},~~k_1,k_2,k_3\in\mathbb Z
$$
A second HINT, hover your mouse over the box to see it, but it might be a spoiler:

 Cyclic groups are Abelian.

