Related papers: On locally finite skew group algebras

In this paper we study the existence of free non-abelian subgroups in non-central permutable subgroups of general skew linear groups and locally finite group algebras.

Let $D$ be a weakly locally finite division ring and $n$ a positive integer. In this paper, we investigate the problem on the existence of non-cyclic free subgroups in non-central almost subnormal subgroups of the general linear group ${\rm…

The study of the existence of free groups in skew linear groups have been begun since the last decades of the 20-th century. The starting point is the theorem of Tits (1972), now often is referred as Tits' Alternative, stating that every…

This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…

This paper studies cluster algebras locally, by identifying a special class of localizations which are themselves cluster algebras. A `locally acyclic cluster algebra' is a cluster algebra which admits a finite cover (in a geometric sense)…

In this paper we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains free non-cyclic subgroups.

The description of the subgroup structure of a non-commutative division ring is the subject of the intensive study in the theory of division rings in particular, and of the theory of skew linear groups in general. This study is still so far…

We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.

Let K be a skew field and (G,<) an ordered group. We show that the skew field generated by the group ring K[G] inside the Malcev-Neumann series ring K((G;<)) contains noncommutative free group algebras.

Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…

We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…

We discuss the possibility of lifting finite subgroups, and in particular finite cyclic subgroups, with respect to the canonical projections between automorphism and outer automorphism groups of free groups, surface groups and their…

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

In this paper, we prove that the multiplicative group of a unital non-commutative Leavitt path algebra $L_K(E)$ and Cohn path algebra $C_K(E)$ contain a non-cyclic free subgroup, provided $K$ is a non-absolute field. We also provide a…

We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in…

We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense.…

Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.

Let $E$ be a graph and $K$ a field. In this paper we prove that the multiplicative group of a unital noncommutative Leavitt path algebra $L_K(E)$ contains non-cyclic free subgroups provided $K$ is of characteristic $0$. Further, we provide…

Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of…