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\begin{document}
\vspace*{-2cm}
\noindent
\hbox{\rule[0.1ex]{\textwidth}{0.03cm}}\vspace*{-0.2cm}
Universit\'e Claude Bernard - Lyon 1, Semestre automne 2023-24, Math{\'e}matiques 3.
\\
Bar{\`e}me Partiel 1.
\centerline{\large\sf{Partiel 1 (1h30) }}\vspace*{0.3cm}
\hbox{\rule[1ex]{\textwidth}{.03cm}}


\section {Cours}  (3\ pt)
Bar{\`e}me:
\\
1a): $0.5/1$ si id{\'e}e g{\'e}n{\'e}rale correcte mais notations confuses.
\\
1b): $1/1$ si rang non d{\'e}fini ou si Dim Im au lieu de rang.
\\
2): $0.5/1$ si une des propri{\'e}t{\'e}s oubli{\'e}e. Tol{\'e}rant si inverse {\`a} gauche ou
{\`a} droite seulement.

\section {Exo 1}  (4\ pt)
Bar{\`e}me:
\\
$4/4$ si vrai argument mentionn{\'e} m{\^e}me si r{\'e}dig{\'e} tr{\`e}s vite.
\\
$2/4$ si "pour certaines valeurs de c c'est un sous-groupe, pour d'autres
non".
\\
$2/4$ si v{\'e}rifi{\'e} que stable par produit et pas fait pour inverse.
\\
$1/4$ si crit{\`e]re de sous-groupe connu mais v{\'e}rification non faite.
\\
$0/4$ Si $+$ au lieu de $*$.

\section {Exo 2}  (4\ pt)
Bar{\`e}me:
\\
$2/4$ Si raisonnement OK mais erreur calcul d{\'e}terminant.
\\
$2/4$ Si d{\'e}terminant bien calcul{\'e} mais embrouille dimensions
\\
$3/4$ Si tout est OK mais th{\'e}or{\`e}me du cours mal cit{\'e} donc par exemple non libre mais pas non g{\'e}n{\'e}ratrice.

\section {Exo 3}  (4*2=8\ pt)
Bar{\`e}me:
\\
a)\ $1/2$ si dimension trouv{\'e}e.
\\
b)\ $1/2$ si raisonnement correct mais erreur b{\^e}te dimensions.
\\
c)\ $1/2$ si raisonnement correct mais erreur b{\^e}te dimensions.
\\
d)\ $1/2$ si raisonnement correct mais erreur b{\^e}te dimensions.


\section {Exo 4}  (3\ pt)
Bar{\`e}me:
\\
$1/3$ si crit{\`e]re de sous-groupe connu mais v{\'e}rification non faite.
\\
$2/3$ si seulement stabilit{\'e} par inverse ou par produit.


\end{document}
