% interface=en output=pdftex
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%\useURL[govern-me][http://sgtrelinst.caib.es/llibrestil/00index.html][][http://sgtrelinst.caib.es/llibrestil/00index.html]
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% hyphenating
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\hyphenation{es-crip-tu-ra}
\hyphenation{ge-ne-ra-lit-za-ció}
\hyphenation{cor-res-po-nents}
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% Modules
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% AMSTHM equivalent
%% Exercici
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  [exercici]
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stopper={.\space},location=serried,left={\bgroup\bf},right={\egroup},width=fit,before={\bgroup\startframedtext[background=screen,frame=off,width=broad]},after={\stopframedtext\egroup}]

%% Lema 
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  [lema]
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%% Proposició, corol·laris, teoremes.
%% Comparteix els nombres amb lema
%% Si volem que vagin a part, hem de posar 'number=proposition'
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  [proposition]
  [lema]
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\defineenumeration
  [corollary]
  [lema]
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\defineenumeration
  [theorem]
  [lema]
  [text={Teorema}]


%% Definició
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  [definition]
  [lema]
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\defineenumeration
  [note]
  [definition]
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%% Demostració

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% Table of contents
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%\setuplist[subsection] %[distance=1em] % section = bold. % 
% Això ho trec d'un manual:
%\setuplist[subsection]
%          [margin=1em,
%          numbercommand=\NumCom]
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% Definitions/abbreviations
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%\define[1]\imp{{\bgroup\startframedtext[background=color,backgroundcolor=lightblue,frame=on,width=broad]#1\stopframedtext\egroup}}


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% Other
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% For putting underline with spaces: \underbar{\dorecurse{40}~}

% Define new register for the Index of Symbols
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% Start the text
\starttext
\version[concept]

\subsubsubject{El problema de la paraula}

\startitemize[1]
\item $\pi(x^{-1}) = \pi(x)^{-1}$ per a tot $x \in X$.
\item Per a tota paraula $w = w_1 \ldots w_r$ sobre $X \cup X^{-1}$,
\startformula
\pi(w) = \pi(w_1) \cdots \pi(w_r) \in G.
\stopformula
\stopitemize



\stoptext

\startitemize[1]
\item $\pi(x^{-1}) = \pi(x)^{-1}$ per a tot $x \in X$.
\item Per a tota paraula $w = w_1 \ldots w_r$ sobre $X \cup X^{-1}$,
\startformula
\pi(w) = \pi(w_1) \cdots \pi(w_r) \in G.
\stopformula
\stopitemize

\startdefinition
Sigui $X$ un conjunt qualsevol i $R \subseteq F(X) \times F(X)$ una relació binària sobre el grup lliure $F(X)$. Una {\em presentació ${\cal P}$ amb generadors $X$ i relacions $R$}\index{presentació}, que indicarem amb ${\cal P} = \langle X \mid R \rangle$, és el grup quocient $F(X)/\langle \langle R_* \rangle \rangle$, on
\startformula
R_* = \{uv^{-1} \mid (u, v) \in R\} \subseteq F(X).
\stopformula
Quan ens convengui diferenciar entre la presentació com a un parell ordenat de símbols i el grup quocient en si, indicarem amb ${\cal P}$ la presentació i $G({\cal P})$ el grup que aquesta representa.
\stopdefinition