Roots of the affine Cremona group

Finite abelian subgroups of the Cremona group of the plane

The Cremona group of the plane is compactly presented

This article shows that the Cremona group of the plane is compactly presented. To do this we prove that it is a generalised amalgamated product of three of its algebraic subgroups (automorphisms of the plane and Hirzebruch surfaces) divided by one relation.

Nonlinearity of Some Subgroups of the Planar Cremona Group

We give some examples of nonlinear subgroups of the planar Cremona group.

Appendix A . The Cremona group is not an amalgam Yves

Let k be a field. The Cremona group Bir(Pk) of k in dimension d is defined as the group of birational transformations of the d-dimensional k-affine space. It can also be described as the group of k-automorphisms of the field of rational functions k(t1, . . . , td). We endow it with the discrete topology. Let us say that a group has Property (FR)∞ if it satisfies the following (1) For every isom...

a note on the affine subgroup of the symplectic group

we examine the symplectic group $sp_{2m}(q)$ and its correspondingaffine subgroup. we construct the affine subgroup and show that itis a split extension. as an illustration of the above we study theaffine subgroup $2^5{:}sp_4(2)$ of the group $sp_6(2)$.