Related papers: Finiteness of algebraic fundamental groups

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

For a finite smooth algebraic group $F$ over a field $k$ and a smooth algebraic group $\bar G$ over the separable closure of $k$, we define the notion of $F$-kernel in $\bar G$ and we associate to it a set of nonabelian 2-cohomology. We use…

We survey new results on finite groups of birational transformations of algebraic varieties.

We use differential forms on loop spaces to prove that the fundamental group of certain geometric transformation groups is infinite. Examples include both finite and infinite dimensional Lie groups. The finite dimensional examples are the…

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group…

We present a complete list of groups $G$ and fields $F$ for which: (i) the group of normalized units V(FG) of the group algebra FG is locally nilpotent; (ii) the group algebra FG has a finite number of nilpotent elements and V(FG) is an…

Let $k(G)$ be the number of conjugacy classes of finite groups $G$ and $\pi_e(G)$ be the set of the orders of elements in $G$. Then there exists a non-negative integer $k$ such that $k(G)=|\pi_e(G)|+k$. We call such groups to be $co(k)$…

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

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…

Let $K$ be an unramified $p$-adic local field and let $W$ be the ring of integers of $K$. Let $(X,S)/W$ be a smooth proper scheme together with a normal crossings divisor. We show that there are only finitely many log crystalline $\mathbb…

In this paper we study arithmetical and structural features of a finite group that possesses exactly two conjugacy class sizes that are composite numbers.

We prove that a log surface has only finitely many weakly log canonical projective models with klt singularities up to log isomorphism, by reducing the problem to the boundedness of their polarization.

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

Here we show that a finite nilpotent group is 2-closed if and only if it is either cyclic or a direct product of a generalized quaternion group with a cyclic group of odd order.

We show the finite generation of certain invariant graded algebras defined on toric weak log Fano fibrations. These are the toric version of FGA algebras, recently introduced by Shokurov in connections to the existence of flips.

The concept of an omnigenous locally finite group was introduced in [2] as a generalization of Hall's universal countable locally finite group. In this paper we show that the class of all countable omnigenous locally finite groups is Borel…

In this article we work out the details of flat groups of the automorphism group of locally finite Bruhat-Tits buildings.

We prove boundedness of global strong $(\delta,n)$-complements for generalized $\epsilon$-log canonical pairs of Fano type. We also prove some partial results towards boundedness of local strong $(\delta,n)$-complements for semi-stable…

We prove that a countable semigroup $S$ is locally finite if and only if the Arens-Michael envelope of its semigroup algebra is a $(DF)$-space. This is a counterpart to a recent result of the author, which asserts that $S$ is finitely…

In this paper we describe all the finite almost simple groups whose Gruenberg--Kegel graphs coincide with Gruenberg--Kegel graphs of finite solvable groups.