Related papers: Chasing finite shadows of infinite groups through …

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

Whereas for a substantial part, Finite Geometry during the past 50 years has focussed on geometries over finite fields, geometries over finite rings that are not division rings have got less attention. Nevertheless, several important…

In this paper, we highlight that the point group structure of elliptic curves over finite or infinite fields, may be also observed on singular cubics with a quadratic component. Starting from this, we are able to introduce in a very general…

We study the realization problem of finite groups as the group of homotopy classes of self-homotopy equivalences of finite spaces. Let $G$ be a finite group. Using an infinite family of pairwise non weakly homotopic asymmetric spaces we…

We introduce a new approach to representation theory of finite groups that uses some basic algebraic geometry and allows to do all the theory without using characters. With this approach, to any finite group $G$ we associate a finite number…

We determine the finite groups whose real irreducible representations have different degrees.

A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…

On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…

A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.

We investigate the relationship between finite groups and incidence geometries through their automorphism structures. Building upon classical results on the realizability of groups as automorphism groups of graphs, we develop a general…

We determine the structure of the finite groups with the property that every cyclic subgroup is the intersection of maximal subgroups, comparing this property with the one where all proper subgroups are intersections of maximal subgroups.

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…

Let $d \geq 2$ be an integer. We conjecture that there is a finitely generated perfect group whose homomorphic images include all finite $d$-generated perfect groups. We prove a special case of this conjecture for the finite perfect groups…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

The convenient setting for smooth mappings, holomorphic mappings, and real analytic mappings in infinite dimension is sketched. Infinite dimensional manifolds are discussed with special emphasis on smooth partitions of unity and tangent…

We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…

We study model geometries of finitely generated groups. If a finitely generated group does not contain a non-trivial finite rank free abelian commensurated subgroup, we show any model geometry is dominated by either a symmetric space of…

A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…

The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…

In various classes of infinite groups, we identify groups that are presentable by products, i.e. groups having finite index subgroups which are quotients of products of two commuting infinite subgroups. The classes we discuss here include…