dotted arrow with a circle in it and a vertical equal sign

Here is the figure I want to draw:

In general I know how to draw a commutative diagram but what I do not know how to draw is the dotted arrow with a circle in it and a vertical equal sign.

Could anyone help me in drawing that please?

• The tikz-cd package offers the possibility to draw dotted arrows: \arrow[d,dotted] should work. For the double line without arrow heads, take a look here: tex.stackexchange.com/a/443023/134144 Jun 13, 2021 at 19:53
• You should show us, what you try so far. Recreate your image is not fun. BTW, this is not your first question about tik-cd (it is not huge, only 18 pages), so it is time, that you read its documentation. It contain examples similar to your problem. Jun 13, 2021 at 20:35
• Ok I just thought that it is understood from my previous posts that I can draw everything in the diagram and it is clear exactly what I am stuck in .... but thanks for the advice and certainly you are correct @Zarko Jun 13, 2021 at 23:23
• Thank you @leandriis your comment is extremely helpful. Jun 13, 2021 at 23:24
• Sorry for typing error, correct is tikz-cd ... Jun 13, 2021 at 23:47

The original diagram is done to 100 % using xy package. In fact I know the classic tips of this package. I add, another solution using xy package leaving the tips untouched. If you want the tips of tikz-cd you can add the cmtip into the square bracket option. Improveding the values of the parameters \xymatrixcolsep{...} and \xymatrixrowsep{...} you can improve the rectangles.

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage[all]{xy}
\begin{document}
{
\xymatrixcolsep{3.5pc}\xymatrixrowsep{3.8pc}
\xymatrix{
\mathbb{Z}\ar[r]^{m}\ar[d]_{\frac nd}  & \mathbb{Z} \ar[r] \ar[d]_{\frac md} &  \mathbb{Z}/m \ar[r]
\ar[r] \ar@{.>}[d]|*+<7pt>[o][F]{\scriptstyle\ell} & 0 \ar@{=}[d]\\
Z\mkern.2mu Z\ar[r]^{n}  & \mathbb{Z} \ar[r] & \mathbb{Z}/n
\ar [r]
\ar [r] &  0,}
}
\end{document}


A solution using stackengine and relsize for the circled ell:

\documentclass{article}
\usepackage{tikz-cd, circledsteps}
\usepackage{mathtools, amsfonts, relsize, stackengine}
\newcommand{\circledell}{\stackinset{c}{}{c}{}{$\ell$}{$\mathlarger{\bigcirc}$}}

\begin{document}

\begin{tikzcd}[column sep=large, row sep=huge]
\mathbb{Z}\dar["\frac{n}{d}",swap]\rar["m"] & \mathbb{Z}\dar["\frac{m}{d}",swap]\rar & \mathbb{Z}/m\dar[dotted, inner sep =3em, "\circledell", description]
\rar & 0 \dar[equal] \\\
Z\:Z\rar["n"] & \mathbb{Z}\rar & \mathbb{Z}/n\rar & 0
\end{tikzcd}

\end{document} \$