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\usepackage{carticle}


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\begin{document}
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\stepcounter{section}
\stepcounter{section}
{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$G_1\neq G$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline163: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
\clearpage
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{\newpage
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{\newpage
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{\newpage
\clearpage
\samepage \begin{displaymath}G=G_0\supset G_1\supset G_2\supset \cdots \supset G_n=\{e\} 
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$G_{i+1}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline177: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
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{\newpage
\clearpage
\samepage \begin{displaymath}G=H_0\supset H_1\supset H_2\supset \ldots \supset H_m=\{e\} 
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$H_j/H_{j+1}$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline187: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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{\newpage
\clearpage
\samepage \begin{definition}\ \, 設 $G$ 為一群。 $G$ 的一正規級數就是一如下之群的鍊鎖:
\begin{displaymath}
G=G_0\supset G_1\supset G_2\supset \ldots \supset G_n=\{e\}
\end{displaymath}
其中，對於每一 $i$,\ $\,$ $G_{i+1}$ 皆為 $G_i$ 之正規子群。
The groups $G_i/G_{i+1}$ are the factor groups of the chain.
The length of the chain is
the number of strict inclusions in the chain. A normal series is a
composition series if each factor group $G_i/G_{i+1}$ is a simple group $\neq \{e\}$. Two normal series are equivalent if there is a one-to-one
correspondence between their factor groups such that corresponding factor
groups are isomorphic.
\end{definition}
}

{\newpage
\clearpage
\samepage \begin{theorem}[Jordan-Holder]
\ \, Any two composition series of a group are equivalent.
\end{theorem}
}

{\newpage
\clearpage
\samepage \begin{equation}\label{one}
G=G_0\supset G_1\supset G_2\supset \ldots \supset G_n=\{e\}
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{equation}\label{two}
G=H_0\supset H_1\supset H_2\supset \ldots \supset H_m=\{e\}
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{equation}\label{three}
G=G_0\supset G_1\supset G_1\cap H_1\supset G_2\cap H_1\supset \ldots \supset
G_n\cap H_1=\{e\}
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{equation}\label{four}
G=H_0\supset H_1\supset H_1\cap G_1\supset H_2\cap G_1\supset \ldots \supset
H_m\cap G_1=\{e\}
\end{equation}
}

{\newpage
\clearpage
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{\newpage
\clearpage
\samepage \begin{displaymath}(G_i\cap H_1)/(G_{i+1}\cap H_1)=(G_i\cap H_1)/(G_{i+1}\cap (G_i\cap
H_1))\approx 
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}G_{i+1}(G_i\cap H_1)/G_{i+1}, 
\end{displaymath}
}

{\newpage
\clearpage
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{\newpage
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{\newpage
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}

{\newpage
\clearpage
\samepage \begin{displaymath}G_1\supset (G_1\cap H_1)\supset (G_2\cap H_1)\supset \ldots \supset (G_n\cap
H_1)=\{e\}, 
\end{displaymath}
}

{\newpage
\clearpage
\samepage \begin{displaymath}G_1\supset G_2\supset \ldots \supset G_n=\{e\}\hbox{,} 
\end{displaymath}
}

{\newpage
\clearpage
\samepage \setbox\sizebox=\hbox{$\cdots$}\lthtmltypeout{latex2htmlSize :tex2html_wrap_inline241: \the\ht\sizebox::\the\dp\sizebox.}\box\sizebox
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\stepcounter{section}
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{\newpage
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\samepage \begin{figure}[htb]
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{\newpage
\clearpage
\samepage \begin{table}[hbp]
\footnotesize
\vglue0pt

\begin{center}
 
 \begin{center}
 

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Tool & \multicolumn{1}{c}{Learning Curve }& \multicolumn{1}{c}{Support             }\\  \noalign{\ifnum0=`}\fi\hrule \@height \arrayrulewidth
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FrameMaker & 5.0 & 6.0 \\   
Troff & 10.0 & 1.0 \\ 
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}

\stepcounter{section}

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