\documentclass[titlepage]{amsbook}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage{amsbsy,amsmath,amssymb}
\usepackage{tikz}
\usetikzlibrary{positioning}
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\usetikzlibrary{shapes.geometric,shapes.arrows,decorations.pathmorphing}
\usetikzlibrary{matrix,chains,scopes,positioning,arrows,fit}
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\begin{document}
\begin{center}
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cercle/.style={circle,draw=black!80!white,fill=black!10!white,thick, inner sep=2pt, text=black},
fletxa/.style={draw=black!80!white,thick}
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%%%%%%%%%%%%%%%%%%
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\node[] () at (7.7,-6) [] {$,\cdots ,$};
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\node[] () at (7.7,-7) [] {$,\cdots ,$};
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\node[] () at (6.15,-6.5) [] {$\scriptscriptstyle\rotatebox{90}{=}$};
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%%%%%%%%%%%%%%%%%%
\tikzset{encercla/.style={draw=hsrmWarmGreyDark, thick, inner sep=0pt, rectangle, rounded corners}};
\node [encercla, fit=(1A) ] {} ;
\node [encercla, fit=(2A) ] {} ;
\node [encercla, fit=(3A)(9A) ] {} ;
\node [encercla, fit=(1B)(3B) ] {} ;
\node [encercla, fit=(4B) ] {} ;
\node [encercla, fit=(5B)(9B) ] {} ;
\node [encercla, fit=(1C)(7C) ] {} ;
\node [encercla, fit=(8C) ] {} ;
\node [encercla, fit=(9C) ] {} ;
\node [encercla, fit=(1a) ] {} ;
\node [encercla, fit=(2a)(6a) ] {} ;
\node [encercla, fit=(7a)(11a) ] {} ;
\node [encercla, fit=(1b)(2b) ] {} ;
\node [encercla, fit=(3b)(7b) ] {} ;
\node [encercla, fit=(8b)(11b) ] {} ;
\node [encercla, fit=(1c)(5c) ] {} ;
\node [encercla, fit=(6c)(10c) ] {} ;
\node [encercla, fit=(11c) ] {} ;
%\draw[draw=hsrmWarmGreyDark, thick, -] (2.5,3) -- (2.5,-3);
\node[] () at (0,-8) [] {$\sigma(({\color{red}{\mathfrak{Q}_{j}}}\circ {\color{blue}{\mathfrak{P}_{j}}})_{j\in n})$};
\node[] () at (7.25,-8) [] {${\color{red}{\sigma((\mathfrak{Q}_{j})_{j\in n})}}\circ {\color{blue}{\sigma((\mathfrak{P}_{j})_{j\in n})}}$};
\end{tikzpicture}
\end{center}
\end{document}
