grandes-ecoles 2015 QI.C.2

grandes-ecoles · France · centrale-maths1__mp Groups Group Homomorphisms and Isomorphisms

We denote by $\mathcal{D}$ the set of affine lines of the plane and we consider the application $\Psi : \left\{ \begin{array}{cll} G & \rightarrow & \mathcal{D} \\ M(A, \vec{b}) & \mapsto \Delta\left(\left\langle A\vec{e}_1, \vec{b}\right\rangle, A\vec{e}_1\right) \end{array} \right.$.
Determine $\Psi\left(M\left(I_2, \overrightarrow{0}\right)\right)$.

We denote by $\mathcal{D}$ the set of affine lines of the plane and we consider the application $\Psi : \left\{ \begin{array}{cll} G & \rightarrow & \mathcal{D} \\ M(A, \vec{b}) & \mapsto \Delta\left(\left\langle A\vec{e}_1, \vec{b}\right\rangle, A\vec{e}_1\right) \end{array} \right.$.

Determine $\Psi\left(M\left(I_2, \overrightarrow{0}\right)\right)$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.C.1 QI.C.2 QI.C.3 QI.C.4 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QIII.A QIII.B QIII.C.1 QIII.C.2 QIII.C.3 QIV.A.1 QIV.A.2 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QIV.D.3 QV.A.1 QV.A.2 QV.A.3 QV.B.1 QV.B.2