Related papers: The Cremona group and its subgroups

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…

We present the abelianisation of the birational transformations of the real projective plane.

We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.

This paper describes in basic terms what a "Thin Group" is, as well as its uses in various subjects.

Two infinite families of Cremona maps depending on one real parameter are given. For all integers $n \ge 1$ the first family of Cremona maps consists of group elements in $Bir \left( \mathbb{P}^{n} \right)$ with bidegree $(n, n)$, the…

In this note we study the finite groups whose subgroup lattices are dismantlable.

In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.

The group of almost Riordan arrays contains the group of Riordan arrays as a subgroup. In this note, we exhibit examples of pseudo-involutions, involutions and quasi-involutions in the group of almost Riordan arrays.

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

We explore to what extent the underlying variety of a connected algebraic group or the underlying manifold of a real Lie group determines its group structure.

This paper serves as an example to show the way we pass from semigroups to $\Gamma$-semigroups and to hypersemigroups.

This short note deals with the conjugacy classes of monomial birational maps in the $n$-dimensional Cremona group, $n\geq 2$.

We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two…

We show that the real Cremona group of the plane is a non-trivial amalgam of two groups amalgamated along their intersection and give an alternative proof of its abelianisation.

This paper develops an approach for describing centrally extended groups, as determining the adjoint groups associated with quandles. Furthermore, we explicitly describe such groups of some quandles. As a corollary, we determine some second…

This paper contains a new proof of the classification of elements of prime order in the Cremona group Bir(P^2), up to conjugation. In addition, we give explicit geometric constructions of these Cremona transformations, and provide a…

We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.

The action of the Cremona group of rank 2 on an infinite dimensional hyperbolic space is the main recent tool to study the Cremona group. Following the analogy with the action of PSL(2,Z) on the Poincar\'e half-plane, we exhibit a…

We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.

We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of…