Related papers: Finite presentations for K\"ahler groups with arbi…

This is a translation. I have added translations for (possibly) outdated definitions in an appendix at the end. In this paper, we define distributive groups and show some properties of them. We then concern ourselves with the homogeinity of…

The underlying complex structure of an ALE K\"ahler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE K\"ahler…

We determine the automorphism group for some well known constructions of finite semifields. In particular, we compute the automorphism group of Sandler's semifields and in certain cases the automorphism groups of the Hughes-Kleinfeld and…

Extended affine Weyl groups are the Weyl groups of extended affine root systems. Finite presentations for extended affine Weyl groups are known only for nullities $\leq 2$, where for nullity 2 there is only one known such presentation. We…

We consider a family of finitely presented groups, called Universal Left Invertible Element (or ULIE) groups, that are universal for existence of one--sided invertible elements in a group ring K[G], where K is a field or a division ring. We…

We study finiteness properties, especially the noetherian property, the Krull dimension and a variation of finite presentation, in categories of polynomial functors from a small symmetric monoidal category whose unit is an initial object to…

Let $G$ be a finitely generated abelian-by-finite group and $k$ a field of characteristic $p\ge 0$. The Euler class $[k_G]$ of $G$ over $k$ is the class of the trivial $kG$-module in the Grothendieck group $G_0(kG)$. We show that $[k_G]$…

The deficiency of a group is the maximum over all presentations for that group of the number of generators minus the number of relators. Every finite group has non-positive deficiency. We show that every non-positive integer is the…

Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only…

We construct examples of complete quaternionic K\"ahler manifolds with an end of finite volume, which are not locally homogeneous. The manifolds are aspherical with fundamental group which is up to an infinite cyclic extension a semi-direct…

PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…

In this paper, we classify the finite simple groups with an abelian Sylow subgroup.

In $2019$ Hyde and the second author constructed the first family of finitely generated, simple, left orderable groups. We prove that these groups are not finitely presentable, non-inner amenable, don't have Kazhdan's property $(T)$ (yet…

The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous…

It was recently proven by Esnault, Shusterman and the second named author, that the \'etale fundamental group of a connected smooth projective variety over an algebraically closed field $k$ is finitely presented. In this note, we extend…

Let $G$ be a finite solvable group. Then $G$ always has a useful presentation, which we call a "long presentation". Using a "long presentation" of $G$, we present an inductive method of constructing the irreducible representations of $G$…

We provide polynomial lower bounds for residual finiteness of residually finite, finitely generated solvable groups that admit infinite order elements in the Fitting subgroup of strict distortion at least exponential. For this class of…

We compute Euler characteristics of p-subgroup categories of finite groups

We construct left invariant special K\"ahler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special K\"ahler Lie algebras according to two linear representations…