Grupos e Corpos

\[ \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\C}{\mathbb C} \newcommand{\F}{\mathbb F} \newcommand{\K}{\mathbb K} \newcommand{\L}{\mathbb L} \newcommand{\N}{\mathbb N} \newcommand{\sym}[1]{\operatorname{Sym}(#1)} \newcommand{\GLV}[1]{\operatorname{GL}(#1)} \newcommand{\SLV}[1]{\operatorname{SL}(#1)} \newcommand{\GL}[2]{\operatorname{GL}(#1,#2)} \newcommand{\SL}[2]{\operatorname{SL}(#1,#2)} \newcommand{\lxor}{\dot\lor} \newcommand{\cond}{\Rightarrow} \newcommand{\bicond}{\Leftrightarrow} \newcommand{\mdc}[2]{\operatorname{mdc}(#1,#2)} \newcommand{\grau}[1]{\operatorname{grau}(#1)} \newcommand{\real}[1]{\mathfrak R(#1)} \newcommand{\imag}[1]{\mathfrak I(#1)} \newcommand{\argz}[1]{\mbox{arg}(#1)} \DeclareMathOperator{\sen}{sen} \newcommand{\cis}[1]{\cos #1+i\sen #1} \newcommand{\E}{\mathbb E} \newcommand{\aut}[1]{\textrm{Aut}(#1)} \newcommand{\fix}[1]{\textrm{Fix}(#1)} \newcommand{\gal}[2]{\textrm{Gal}(#1:#2)} \newcommand{\overbar}[1]{\mkern 1.5mu\overline{\mkern-1.5mu#1\mkern-1.5mu}\mkern 1.5mu} \newcommand{\ul}[1]{\underline{#1}} \newcommand{\tn}[1]{\textnormal{#1}} \]