Related papers: On homomorphic images of ultraproducts

We study certain subgroups of the full group of Hopf algebra automorphisms of a biproduct. In the process interesting subgroups of certain permutation groups come into play.

We consider metric ultraproducts of finite groups with respect to some classes of length functions. All sofic groups embed into these ultraproducts. We study embeddings of normed groups. We also show that in some natural situations such an…

There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation…

We study properties of a group, abelian group, ring, or monoid $B$ which (a) guarantee that every homomorphism from an infinite direct product $\prod_I A_i$ of objects of the same sort onto $B$ factors through the direct product of finitely…

Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

Bergman has given the following abstract characterisation of the inner automorphisms of a group $G$: they are exactly those automorphisms of $G$ which can be extended functorially along any homomorphism $G \rightarrow H$ to an automorphism…

The holomorph of a discrete group $G$ is the universal semi-direct product of $G$. In chapter 1 we describe why it is an interesting object and state main results. In chapter 2 we recall the classical definition of the holomorph as well as…

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…

New results on metric ultraproducts of finite simple groups are established. We show that the isomorphism type of a simple metric ultraproduct of groups $X_{n_i}(q)$ ($i\in I$) for $X\in\{{\rm PGL},{\rm PSp},{\rm PGO}^{(\varepsilon)},{\rm…

We construct homology theories with coefficients in L-spectra on the category of ball complexes and we define products in this setting. We also obtain signatures of geometric situations in these homology groups and prove product formulae…

Computations in the cohomology of finite groups.

We consider associative superalgebra realized on the smooth Grassmann-valued functions with compact supports in R^n. The lower Hochschild cohomologies of this superalgebra are found.

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.

We present some results about quasiconvex subgroups of infinite index and their products. After that we extend the standard notion of a subgroup commensurator to an arbitrary subset of a group, and generalize some of the previously known…

The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…

This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.

This is an expanded version of the talk I gave at Oberwolfach, MIT and several other universities.

In this note, we show a uniqueness result of homogeneous quasimorphisms defined on the universal cover of the symplectic linear group.