讲义: 抽象代数(于品)/preamble

\theoremstyle{plain}
\newtheorem{them}{定理}
\newtheorem{lem}{引理}
\newtheorem{prop}{命题}
\newtheorem{coro}{推论}

\theoremstyle{definition}
%\newtheorem{defn}{定义}[section]
%\newtheorem{exam}{例子}[section]
%\newtheorem{rem}{注记}[section]
\newtheorem{defn}{定义}
\newtheorem{exam}{例子}
\newtheorem{rem}{注记}

\newtheorem*{app}{应用}
% \newtheorem*{note}{{\small{附注}}}
%\newtheorem{exer}{练习}[section]
\newtheorem{exer}{练习}

\theoremstyle{remark}
\newtheorem*{wisdom}{寄语}

\def\R{{\mathbb{R}}}
\def\Q{{\mathbb{Q}}}
\def\C{{\mathbb{C}}}
\def\Z{{\mathbb{Z}}}

\def\End{{\mathbf{End}}}
\def\Stab{{\rm Stab}}
\def\orb{{\rm orb}}
\def\Int{{\rm Int}}

\def\Hom{\mathbf{Hom}}
\def\Ker{{\rm Ker}}
\def\Aut{\mathbf{Aut}}
\def\Out{\mathbf{Out}}

\def\Gal{{\mathbf{Gal}}}
\def\F{{\mathbb{F}}}
\def\Zp{{\faktor{\mathbb{Z}}{p\mathbb{Z}}}}
\def\Zfive{{\faktor{\mathbb{Z}}{5\mathbb{Z}}}}
\def\Zn{{\faktor{\mathbb{Z}}{n\mathbb{Z}}}}

\def\Fp{{\mathbb{F}_p}}
\def\char{{\rm Char}}
\def\gal{\mathbf{Gal}}
\def\GL{{\mathbf{GL}}}
\def\SL{{\mathbf{SL}}}
\def\PGL{{\mathbf{PGL}}}
\def\PSL{{\mathbf{PSL}}}

\def\psylow{{Sylow $p$-子群}}

\def\thetheorem{\thmprefix\arabic{theorem}}%
\def\@nextsection{}% undo numberwithin{theorem}{section}

%this \faktor works both in math and tikzcd
\newcommand*{\faktor}[2]{% \newfaktor{#1}{#2} -> #1/#2
  \mathord{\raisebox{0.27em}{$#1$}% Numerator
  \!\!\!\: \diagup \!\!\!\; %Slash /
  \raisebox{-0.27em}{$#2$}% Denominator
  }%
}
\newcommand*{\mfaktor}[2]{% \newfaktor{#1}{#2} -> #1/#2
  \mathord{\raisebox{-0.27em}{$#1$}% Numerator
  \!\!\:\diagdown\!\! %Slash /
  \raisebox{0.27em}{$#2$}% Denominator
  }%
}