The Geometries Associated with a Certain System of Cremona Groups

Plane Geometries Associated with Certain 2-Transitive Groups*

Let G be a permutation group 2-transitive on a finite set. Assume that the stabilizer of two points fixes exactly K 3 3 points, but not all points. Let L denote this set of K points, and call the distinct sets Lg, g E G, lines. Then all lines have K points, and any two different points are in a unique line. This means that we have a design 9 (with h = 1). The only known possibilities for 9 are ...

a study on construction of iranian life tables: the case study of modified brass logit system

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Tori in the Cremona Groups

We classify up to conjugacy the subgroups of certain types in the full, in the affine, and in the special affine Cremona groups. We prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results in the Linearization Problem generalizing to disconnected group Bia lynicki-Birula’s results of 1966–67. We prove “fusion theorems” for n-dimensional tori in the a...

Some Subgroups of the Cremona Groups

We explore algebraic subgroups of the Cremona group Cn over an algebraically closed field of characteristic zero. First, we consider some class of algebraic subgroups of Cn that we call flattenable. It contains all tori. Linearizability of the natural rational actions of flattenable subgroups on An is intimately related to rationality of the invariant fields and, for tori, is equivalent to it. ...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup