Related papers: Nonlinearity of some subgroups of the planar Cremo…

We study finite non-linearizable subgroups of the plane Cremona group which potentially could be stably linearizable.

We describe the nilpotent subgroups of the group Bir(P^2(C)) of birational transformations of the complex projective plane. Let N be a nilpotent subgroup of class k>1; then either each element of N has finite order, or N is virtually…

We prove that, except for a few cases, stable linearizability of finite subgroups of the plane Cremona group implies linearizability.

The aim of this paper is to give a finer geometric description of the algebraic varieties parametrizing conjugacy classes of nonsolvable subgroups in the plane Cremona group.

We survey aspects of locally nilpotent linear groups. Then we obtain a new classification; namely, we classify the irreducible maximal locally nilpotent subgroups of $\mathrm{GL}(q, \mathbb F)$ for prime $q$ and any field $\mathbb F$.

In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.

We obtain a sharp bound for p-elementary subgroups in the plane Cremona group over an arbitrary perfect field.

We classify, up to conjugacy, the subgroups of the Cremona group isomorphic to (Z/p)^r, where p is prime and r is maximal.

In this paper we describe conjugacy classes of finite subgroups of odd order in the group of birational automorphisms of the real projective plane.

The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other…

The structure of a group which is not nilpotent but all of whose proper subgroups are nilpotent has interested the researches of several authors both in the finite case and in the infinite case. The present paper generalizes some classic…

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, in the nilpotent case. It turns out that in the o-minimal context, like for finite groups, nilpotency is equivalent to…

We characterize those modular group algebras FG whose group of unitary units is locally nilpotent under the classical involution of FG.

The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a…

In this paper, we establish the theory of nilpotent hypergroups and study some properties of nilpotent hypergroups and provided some structural characterizations of nilpotent hypergroups.

We study the algebraic structure of the $n$-dimensional Cremona group and show that it is not an algebraic group of infinite dimension (ind-group) if $n\ge 2$. We describe the obstruction to this, which is of a topological nature. By…

The Cremona groups are the groups of all birational equivalences of rational varieties and, equivalently, the automorphism groups of the rational function fields. In this note, we explain that homological stability fails for them in both…

We investigate some situation in which automorphisms of a group G are uniquely determined by their restrictions to a proper subgroup H. Much of the paper is devoted to studying under which additional hypotheses this property forces G to be…

Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is…

We provide a detailed structural description of the nilpotent primitive subgroups of $\mathrm{GL}(n, \mathbb{F})$, where $\mathbb{F}$ is a finite field.