Não tenho certeza de como enviar uma mensagem de texto para o isomorfismo com notas em LaTeX. É assim que mostro a parte do isomorfismo no Latex. Mas não sei como adicionar conteúdo verde a ele.
\documentclass{article}
\usepackage{amssymb}
\usepackage{tikz}
\newcommand{\quo}[2]{{\raisebox{.2em}{$#1$}\left/\raisebox{-.2em}{$#2$}\right.}} % The quotient of elements or groups
\begin{document}
$\quo{HK}{K}\simeq\quo{H}{H\cap K}$\\
\end{document}
Responder1
Veja isto, por exemplo:
\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{mathtools}
\newcommand{\quo}[2]{{\raisebox{.2em}{$#1\!$}\left/\raisebox{-.2em}{$#2$}\right.}} % The quotient of elements or groups
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\usetikzlibrary{calc,tikzmark}
\tikzset{%
pics/mybraces/.style args={#1/#2}{code={%
\draw [decorate,decoration={brace,amplitude=4pt,#2},rotate=#1] (0,0) -- (0,1);
}},
pics/mybraces/.default=30/{}
}
\begin{document}
You can do whatever you want with \LaTeX{}:
\[
\underbrace{\quo{\overbrace{HK}^{G}}{K}}_{\mathllap{\mathrm{PGL}(2,\mathbb{C})\text{: projective linear group}}} \simeq \overbrace{\quo{H}{H\cap K}}^{\mathrlap{\mathrm{PSL}(2,\mathbb{C})\text{: projective special linear group}}}\mkern-58mu \underbrace{\phantom{\raisebox{-.2em}{$H\cap K$}}}_{\{\pm I_2\}}
\]
You can use also \textbackslash{}\texttt{tikzmark}:
\[
\tikzmark{leftpoint}\quo{\overbrace{HK}^{G}}{K} \simeq \quo{H}{H\cap K}\tikzmark{rightpoint}\mkern-58mu \underbrace{\phantom{\raisebox{-.2em}{$H\cap K$}}}_{\{\pm I_2\}}
\]
\begin{tikzpicture}[overlay,remember picture]
\pic at ($(pic cs:leftpoint)+(4pt,-2.5ex)$) {mybraces};
\node[text width=100pt, align=right] at ($(pic cs:leftpoint)+(-60pt,-1.5ex)$) {$_{\mathrm{PGL}(2,\mathbb{C})\text{:}}$\\ \scriptsize projective linear group};
\pic at ($(pic cs:rightpoint)+(7pt,-1ex)$) {mybraces={30/mirror}};
\node[text width=130pt, align=left] at ($(pic cs:rightpoint)+(75pt,3ex)$) {$_{\mathrm{PSL}(2,\mathbb{C})\text{:}}$\\ \scriptsize projective special linear group};
\end{tikzpicture}%
However, as Andrew Swan \& Co. already told you, in your case something like this is better:
\begin{align*}
\quo{HK}{K}&\simeq \quo{H}{H\cap K}
\intertext{where:}
HK &= G \\
\intertext{the projective linear group is represented by:}
\quo{HK}{K}&= \mathrm{PGL}(2,\mathbb{C})
\intertext{the projective special linear group is represented by:}
\quo{H}{H\cap K}&= \mathrm{PSL}(2,\mathbb{C})
\intertext{and}
H\cap K&=\{\pm I_2\}
\end{align*}
\end{document}
Responder2
Conforme comentário de Andrew Swann, você deve explicar a fórmula com algumas palavras. De qualquer forma, acho que você pode usar isso:
\begin{equation}
\underbrace{HK}_{G}/\underbrace{K}_{\mathrm{PGL}(2,\mathbb{C})} \simeq \underbrace{H}_{PSL(2,\mathbb{C})}/\underbrace{H\cap K}_{\pm I_2}
\end{equation}