diff options
Diffstat (limited to 'ga/n4.lyx')
| -rw-r--r-- | ga/n4.lyx | 20 |
1 files changed, 10 insertions, 10 deletions
@@ -745,7 +745,7 @@ Si \end_inset es una familia de grupos, -\begin_inset Formula $\bigoplus_{i\in I}G_{i}:=\{(g_{i})_{i\in I}\in\prod_{i\in I}G_{i}:\{i\in I:g_{i}\ne1\}\text{ es finito}\}$ +\begin_inset Formula $\bigoplus_{i\in I}G_{i}:=\{(g_{i})_{i\in I}\in\prod_{i\in I}G_{i}\mid \{i\in I\mid g_{i}\ne1\}\text{ es finito}\}$ \end_inset es un subgrupo de @@ -773,7 +773,7 @@ centralizador \end_inset es el subgrupo -\begin_inset Formula $C_{G}(x):=\{g\in G:gx=xg\}$ +\begin_inset Formula $C_{G}(x):=\{g\in G\mid gx=xg\}$ \end_inset , y el @@ -785,7 +785,7 @@ centro \end_inset es el subgrupo abeliano -\begin_inset Formula $Z(G):=\{g\in G:\forall x\in G,gx=xg\}=\bigcap_{x\in X}C_{G}(x)$ +\begin_inset Formula $Z(G):=\{g\in G\mid \forall x\in G,gx=xg\}=\bigcap_{x\in X}C_{G}(x)$ \end_inset . @@ -2973,7 +2973,7 @@ estabilizador \end_inset a -\begin_inset Formula $\text{Estab}_{G}(x):=\{g\in G:g\cdot x=x\}$ +\begin_inset Formula $\text{Estab}_{G}(x):=\{g\in G\mid g\cdot x=x\}$ \end_inset . @@ -3014,7 +3014,7 @@ estabilizador \end_inset a -\begin_inset Formula $\text{Estab}_{G}(x):=\{g\in G:x\cdot g=x\}$ +\begin_inset Formula $\text{Estab}_{G}(x):=\{g\in G\mid x\cdot g=x\}$ \end_inset . @@ -3050,7 +3050,7 @@ acción por translación a la izquierda y \begin_inset Formula \[ -\text{Estab}_{G}(xH)=\{g\in G:gxH=xH\}=\{g\in G:x^{-1}gx\in H\}=xHx^{-1}=H^{x^{-1}}. +\text{Estab}_{G}(xH)=\{g\in G\mid gxH=xH\}=\{g\in G\mid x^{-1}gx\in H\}=xHx^{-1}=H^{x^{-1}}. \] \end_inset @@ -3170,7 +3170,7 @@ normalizador \end_inset es -\begin_inset Formula $N_{G}(H):=\text{Estab}_{G}(H)=\{g\in G:H^{g}=H\}$ +\begin_inset Formula $N_{G}(H):=\text{Estab}_{G}(H)=\{g\in G\mid H^{g}=H\}$ \end_inset , el mayor subgrupo de @@ -3393,12 +3393,12 @@ status open \begin_layout Plain Layout Si la acción es por la izquierda, -\begin_inset Formula $\text{Estab}_{G}(x)^{g^{-1}}=\{ghg^{-1}:h\cdot x=x\}=\{p\in G:g^{-1}pg\cdot x=x\}=\{p\in G:p\cdot(g\cdot x)=g\cdot x\}=\text{Estab}_{G}(g\cdot x)$ +\begin_inset Formula $\text{Estab}_{G}(x)^{g^{-1}}=\{ghg^{-1}\mid h\cdot x=x\}=\{p\in G\mid g^{-1}pg\cdot x=x\}=\{p\in G\mid p\cdot(g\cdot x)=g\cdot x\}=\text{Estab}_{G}(g\cdot x)$ \end_inset . Si es por la derecha, -\begin_inset Formula $\text{Estab}_{G}(x)^{g}=\{g^{-1}hg:x\cdot h=x\}=\{p\in G:x\cdot gpg^{-1}=x\}=\{p\in G:(x\cdot g)\cdot p=x\cdot g\}$ +\begin_inset Formula $\text{Estab}_{G}(x)^{g}=\{g^{-1}hg\mid x\cdot h=x\}=\{p\in G\mid x\cdot gpg^{-1}=x\}=\{p\in G\mid (x\cdot g)\cdot p=x\cdot g\}$ \end_inset . @@ -3606,7 +3606,7 @@ status open Demostración: \series default Sea -\begin_inset Formula $X:=\{(g_{1},\dots,g_{p})\in G^{p}:g_{1}\cdots g_{p}=1\}$ +\begin_inset Formula $X:=\{(g_{1},\dots,g_{p})\in G^{p}\mid g_{1}\cdots g_{p}=1\}$ \end_inset , |