File:Lattice diagram of Q adjoin the positive square roots of 2 and 3, its subfields, and Galois groups.svg
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DescriptionLattice diagram of Q adjoin the positive square roots of 2 and 3, its subfields, and Galois groups.svg | |
Source |
Created in LaTeX by the following code: \documentclass[12pt]{article}
\thispagestyle{empty}
\usepackage{tikz}
\usepackage{amsfonts}
\begin{document}
\begin{tikzpicture}[node distance=2cm]
\node (Q) {$\mathbb{Q}$};
\node (Q6) [above of=Q] {$\mathbb{Q}(\sqrt{6})$};
\node (Q2) [right of=Q6] {$\mathbb{Q}(\sqrt{2})$};
\node (Q3) [left of=Q6] {$\mathbb{Q}(\sqrt{3})$};
\node (Q23) [above of=Q6] {$\mathbb{Q}(\sqrt{2}, \sqrt{3})$};
\node (1f) [right of=Q2] {$\{1, f\}$};
\node (1fg) [right of=1f] {$\{1, fg\}$};
\node (1g) [right of=1fg] {$\{1, g\}$};
\node (G) [below of=1fg] {$\{1, f, g, fg\}$};
\node (1) [above of=1fg] {$\{1\}$};
\draw (Q) -- (Q2);
\draw (Q) -- (Q3);
\draw (Q) -- (Q6);
\draw (Q2) -- (Q23);
\draw (Q3) -- (Q23);
\draw (Q6) -- (Q23);
\draw (G) -- (1f);
\draw (G) -- (1fg);
\draw (G) -- (1g);
\draw (1f) -- (1);
\draw (1fg) -- (1);
\draw (1g) -- (1);
\end{tikzpicture}
\end{document}
|
Author | Self |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 01:19, 10 March 2011 | 399 × 164 (32 KB) | Bender2k14 (talk | contribs) | {{Information |Description ={{en|1=Lattice of subgroups and subfields showing their corresponding Galois groups. }} |Source =Created in LaTeX by the following code: <code> \document |
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