From 908911986079fb4bb0414bd035a49c5e6413e3a9 Mon Sep 17 00:00:00 2001
From: Juan Marín Noguera <juan.marinn@um.es>
Date: Wed, 27 May 2020 12:54:14 +0200
Subject: Comentadas las demostraciones que no entran

---
 ga/n4.lyx | 279 ++++++++++++++++++++++++++++++++++++++++++++------------------
 1 file changed, 197 insertions(+), 82 deletions(-)

(limited to 'ga/n4.lyx')

diff --git a/ga/n4.lyx b/ga/n4.lyx
index d2753ea..0d54a67 100644
--- a/ga/n4.lyx
+++ b/ga/n4.lyx
@@ -399,7 +399,8 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Description
 \begin_inset Formula $1\implies2\implies3,4\implies5]$
@@ -441,6 +442,11 @@ Si
  es un grupo con el mismo 1.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Si 
 \begin_inset Formula $S$
@@ -987,7 +993,8 @@ normal
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
 \begin_layout Description
 \begin_inset Formula $1\iff2\iff3\implies4,5]$
@@ -1087,6 +1094,11 @@ normal
  Por simetría con los dos anteriores.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Si 
 \begin_inset Formula $N\leq G$
@@ -1167,10 +1179,10 @@ Si
 \end_inset
 
  tiene índice 2, es normal.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Como las clases por la izquierda módulo 
 \begin_inset Formula $H$
 \end_inset
@@ -1194,16 +1206,20 @@ Como las clases por la izquierda módulo
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula ${\cal SL}_{n}(\mathbb{R})\unlhd{\cal GL}_{n}(\mathbb{R})$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si 
 \begin_inset Formula $a,b\in{\cal GL}_{n}(\mathbb{R})$
 \end_inset
@@ -1219,7 +1235,11 @@ Si
  si y sólo si tienen igual determinante.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 
 \series bold
@@ -1396,42 +1416,50 @@ Propiedades: Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $f(1)f(1)=f(1\cdot1)=f(1)=f(1)1\implies f(1)=1$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(a)^{-1}=f(a^{-1})$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 \begin_inset Formula $f(a)f(a^{-1})=f(aa^{-1})=f(1)=1$
 \end_inset
 
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(a_{1}\cdots a_{n})=f(a_{1})\cdots f(a_{n})$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $n=0$
 \end_inset
@@ -1452,16 +1480,20 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(a^{m})=f(a)^{m}$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $m=0$
 \end_inset
@@ -1491,7 +1523,11 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $f$
@@ -1502,10 +1538,10 @@ Si
 \end_inset
 
  también.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sean 
 \begin_inset Formula $x,y\in H$
 \end_inset
@@ -1525,16 +1561,20 @@ Sean
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $g\circ f:G\to K$
 \end_inset
 
  es un homomorfismo de grupos.
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Para 
 \begin_inset Formula $a,b\in G$
 \end_inset
@@ -1546,7 +1586,11 @@ Para
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f^{-1}(H')\leq G$
 \end_inset
@@ -1566,10 +1610,10 @@ Para
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Claramente 
 \begin_inset Formula $1\in f^{-1}(H')$
 \end_inset
@@ -1617,13 +1661,13 @@ ab^{-1}=f^{-1}(f(ab^{-1}))=f^{-1}(f(a)f(b)^{-1}),
 \end_inset
 
 .
-\begin_inset Newpage pagebreak
+\end_layout
+
 \end_inset
 
 
 \end_layout
 
-\end_deeper
 \begin_layout Enumerate
 \begin_inset Formula $f$
 \end_inset
@@ -1633,9 +1677,9 @@ ab^{-1}=f^{-1}(f(ab^{-1}))=f^{-1}(f(a)f(b)^{-1}),
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1672,6 +1716,7 @@ Como
 .
 \end_layout
 
+\begin_deeper
 \begin_layout Enumerate
 \begin_inset Argument item:1
 status open
@@ -1709,6 +1754,11 @@ Si
 \end_layout
 
 \end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $f(G')\leq H$
 \end_inset
@@ -1732,10 +1782,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Claramente 
 \begin_inset Formula $1\in f(G')$
 \end_inset
@@ -1797,7 +1847,11 @@ Claramente
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Algunos homomorfismos:
 \end_layout
@@ -2027,13 +2081,6 @@ Si
 \end_inset
 
 
-\end_layout
-
-\begin_layout Standard
-\begin_inset Newpage newpage
-\end_inset
-
-
 \end_layout
 
 \begin_layout Standard
@@ -2069,10 +2116,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 La norma 
 \begin_inset Formula $|\cdot|:\mathbb{C}^{*}\to\mathbb{R}^{*}$
 \end_inset
@@ -2088,16 +2135,20 @@ La norma
 , y aplicamos el primer teorema de isomorfía.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula ${\cal GL}_{n}(\mathbb{R})/{\cal SL}_{n}(\mathbb{R})\cong\mathbb{R}^{*}$
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 El determinante 
 \begin_inset Formula $\det:{\cal GL}_{n}(\mathbb{R})\to\mathbb{R}$
 \end_inset
@@ -2113,7 +2164,11 @@ El determinante
 , y aplicamos el primer teorema de isomorfía.
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 En general, 
 \begin_inset Formula $H,K\leq G$
@@ -2124,7 +2179,11 @@ En general,
 \end_inset
 
 .
- En efecto, si 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+En efecto, si 
 \begin_inset Formula $\sigma,\tau\in S_{3}$
 \end_inset
 
@@ -2171,6 +2230,11 @@ En general,
 , luego esto no es un grupo.
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Orden de un elemento
 \end_layout
@@ -2291,6 +2355,11 @@ Si
 
 \end_inset
 
+
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
 En efecto, sean 
 \begin_inset Formula $m:=|a|$
 \end_inset
@@ -2314,6 +2383,11 @@ En efecto, sean
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Si 
 \begin_inset Formula $G=\langle a\rangle$
@@ -3187,10 +3261,10 @@ Sean
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Como 
 \begin_inset Formula $1\cdot x=x$
 \end_inset
@@ -3219,7 +3293,11 @@ Como
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 \begin_inset Formula $[G:\text{Estab}_{G}(x)]=|G\cdot x|$
 \end_inset
@@ -3234,10 +3312,10 @@ Como
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Sea 
 \begin_inset Formula $H:=\text{Estab}_{G}(x)$
 \end_inset
@@ -3278,7 +3356,11 @@ Sea
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si la acción es por la izquierda, 
 \begin_inset Formula $\text{Estab}_{G}(g\cdot x)=\text{Estab}_{G}(x)^{g^{-1}}$
@@ -3306,10 +3388,10 @@ Si la acción es por la izquierda,
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Si la acción es por la izquierda, 
 \begin_inset Formula $\text{Estab}_{G}(x)^{g^{-1}}=\{ghg^{-1}:h\cdot x=x\}=\{p\in G:g^{-1}pg\cdot x=x\}=\{p\in G:p\cdot(g\cdot x)=g\cdot x\}=\text{Estab}_{G}(g\cdot x)$
 \end_inset
@@ -3322,7 +3404,11 @@ Si la acción es por la izquierda,
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Enumerate
 Si 
 \begin_inset Formula $R$
@@ -3333,10 +3419,10 @@ Si
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_deeper
-\begin_layout Standard
+\begin_layout Plain Layout
 Se debe a que las órbitas forman una partición de 
 \begin_inset Formula $X$
 \end_inset
@@ -3344,7 +3430,11 @@ Se debe a que las órbitas forman una partición de
 .
 \end_layout
 
-\end_deeper
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 Así, si 
 \begin_inset Formula $G$
@@ -3404,7 +3494,17 @@ Dado un número primo
 \begin_inset Formula $p$
 \end_inset
 
-, y por el teorema de Lagrange, un grupo finito es un 
+, y 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+por el teorema de Lagrange, 
+\end_layout
+
+\end_inset
+
+un grupo finito es un 
 \begin_inset Formula $p$
 \end_inset
 
@@ -3430,7 +3530,11 @@ Si
 \end_inset
 
 .
- En efecto, si 
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
+En efecto, si 
 \begin_inset Formula $X\subseteq G$
 \end_inset
 
@@ -3466,6 +3570,11 @@ Si
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Standard
 
 \series bold
@@ -3488,9 +3597,10 @@ Teorema de Cauchy:
 \end_inset
 
 .
-\end_layout
+\begin_inset Note Comment
+status open
 
-\begin_layout Standard
+\begin_layout Plain Layout
 
 \series bold
 Demostración:
@@ -3584,7 +3694,7 @@ Demostración:
 .
 \end_layout
 
-\begin_layout Standard
+\begin_layout Plain Layout
 Como 
 \begin_inset Formula $|\sigma|=p$
 \end_inset
@@ -3670,6 +3780,11 @@ Como
 .
 \end_layout
 
+\end_inset
+
+
+\end_layout
+
 \begin_layout Section
 Teoremas de Sylow
 \end_layout
-- 
cgit v1.2.3