Related papers: Finite Localities III
This paper continues the development of the theory of finite localities that was begun in "Finite Localities I". The emphasis in this Part 2.
This paper concerns partial groups, objective partial groups, and (finite) localities, with special attention given to the quotient of a locality by a partial normal subgroup.
We introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
This is a continuation of Part I.
We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…
We describe structure of locally finite groups of finite centraliser dimension.
This paper gives a systematic construction of certain covers of finite semigroups. These covers will be used in future work on the complexity of finite semigroups.
The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…
We classify quasi-simple finite groups of essential dimension 3.
We classify the finite connected-homogeneous digraphs, as well as the infinite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.
We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…
In this article we prove results about finite soluble groups that act with fixity 2 or 3.
In this paper, we consider surfaces in the 3-dimensional Euclidean space E3 which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important…
This article contains a basic introduction to the local study of finite groups, including a brief perspective on the theory of fusion systems and $p$-local finite groups. -- Este art\'iculo contiene una introducci\'on b\'asica al estudio…
We classify the metric spaces that can be approximated by finite homogeneous ones.
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…
The basic properties of locally finite triangulated categories are discussed. The focus is on Auslander--Reiten theory and the lattice of thick subcategories.
We compute the integral third homology of most of the sporadic finite simple groups and of their central extensions.
New expansions of the number zeta(3) in continuous fractions are found.