Related papers: Three plots about the Cremona groups
We give a sharp bound for orders of elementary abelian 2-groups of birational automorphisms of rationally connected threefolds.
We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.
The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.
This paper grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we define a new class of groups. These…
We present some (unfortunately not all) known properties on the Cremona group; when it's possible we mentioned links with the most known group of polynomial automorphisms of the affine plane. The mentioned properties are essentially…
Computations in the cohomology of finite groups.
This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…
We classify all finite simple subgroups in the Cremona group of rank 3
For perfect fields $k$ satisfying $[\bar k:k]>2$, we construct new normal subgroups of the plane Cremona group and provide an elementary proof of its non-simplicity, following the melody of the recent proof by Blanc, Lamy and Zimmermann…
The paper considers computable Folner sequences in computably enumerable amenable groups. We extend some basic results of M. Cavaleri on existence of such sequences to the case of groups where finite generation is not assumed. We also…
In this note we determine the finite groups that can be written as the union of any three irredundant/distinct proper subgroups. The finite groups that can uniquely be written as the union of three proper subgroups are also characterized.
There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation…
We complete the classical and modern work on the classification of conjugacy classes of finite subgroups of the group of birational transformations of the complex projective plane.
We give an explicit set of generators for various natural subgroups of the real Cremona group Bir_R(P^2). This completes and unifies former results by several authors.
This is a continuation of an earlier preprint (math.GT/0209121) under the same title. These papers grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or…
The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a non-commutative ring that is an analog of non-commutative field of two independent variables and prove that the Cremona group…
We investigate some properties of topological groups related to disconnectedness or Archimedeanness. We prove or disprove the preservation of those under operations as subgroups, quotients, products, etc. Characterizations of…
Various connections between the theory of permutation groups and the theory of topological groups are described. These connections are applied in permutation group theory and in the structure theory of topological groups. The first draft of…
This work presents the conjugacy classes of finite abelian subgroups of the Cremona group of the plane. Using a well-known theory, this problem amounts to the study of automorphism groups of some Del Pezzo surfaces and conic bundles. We…
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a…