Related papers: Finite Localities III
In this paper, we continue the classification of finite type Gauss map surfaces in the 3-dimensional Euclidean space $\mathbb{E}^{3}$. We present an important family of surfaces, namely, tubes in $\mathbb{E}^{3}$. We show that the Gauss map…
In this paper, we classify the finite simple groups with an abelian Sylow subgroup.
In this note we study a class of finite groups for which the orders of subgroups satisfy a certain inequality. In particular, characterizations of the well-known groups $\mathbb{Z}_2\times\mathbb{Z}_2$ and $S_3$ are obtained.
The purpose of this paper is to explore the concept of localization, which comes from homotopy theory, in the context of finite simple groups. We give an easy criterion for a finite simple group to be a localization of some simple subgroup…
We show that the finiteness of the fundamental groups of the smooth locus of lower dimensional log Fano pairs would imply the finiteness of the local fundamental group of klt singularities. As an application, we verify that the local…
We show that silting modules are closely related with localisations of rings. More precisely, every partial silting module gives rise to a localisation at a set of maps between countably generated projective modules and, conversely, every…
On objects of a triangulated category with a stability condition, we construct a topology.
In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.
We give an explicit bound on orders of finite subgroups of Cremona group of rank three over $\mathbb{Q}$.
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…
A classification of finite groups in which every 3-maximal subgroup is K-U-subnormal is given.
We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.
We show that if the neighbor complex, as defined by H.~Scarf, of an infinite subset of $\Z^n$ has finite dimension, then each vertex has finitely many neighbors.
In this note, finite type epimorphisms of rings are characterized.
We discuss the notion of essential dimension of a finite group and explain its relation with birational algebraic geometry. We show how this leads to a (partial) classification of simple finite groups of essential dimension less than or…
In this paper, we obtain classification of the topological holonomy groups in $SO(3)$. Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by…
In this paper, we finished the classification of three-generator finite $p$-groups $G$ such that $\Phi(G)\le Z(G)$. This paper is a part of classification of finite $p$-groups with a minimal non-abelian subgroup of index $p$, and partly…
We construct examples of localizations in the category of groups which take the Mathieu group $M_{11}$ to groups of arbitrarily large cardinality which are ``abelian up to finitely many generators''. The paper is part of a broader study on…
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.
We classify finite groups $G$ in $\mathrm{PGL}_{4}(\mathbb{C})$ such that $\mathbb{P}^3$ is $G$-birationally rigid.