Related papers: Finite Localities III
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 finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.
This survey article is intended as an introduction to the recent categorical classification theorems of the three authors, restricting to the special case of the category of modules for a finite group.
We classify all finite simple subgroups in the Cremona group of rank 3
In this paper, we present a construction from a Reedy category $C$ of a direct category $\operatorname{Down}(C)$ and a functor $\operatorname{Down}(C) \to C$, which exhibits $C$ as an $(\infty,1)$-categorical localization of…
A new definition for the notion of a (general) $\infty$-category is given.
We complete the classification of the finite special linear groups $\SL_n(q)$ which are $(2,3)$-generated, i.e., which are generated by an involution and an element of order $3$. This also gives the classification of the finite simple…
A semigroup variety V is said to be locally K-finite, where K stands for any of Green's relations H, R, L, D, or J, if every finitely generated semigroup from V has only finitely many K-classes. We characterize locally K-finite varieties of…
We study various topics, e.g. accumulation points by a mean, two types of derivative by a mean, two new continuity and a boundedness concepts, we construct new means from old ones, finally we investigate the limit of means.
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate…
A finitely generated solvable group with unbounded iterated identity is constructed.
A p-local finite group consists of a finite p-group S, together with a pair of categories which encode ``conjugacy'' relations among subgroups of S, and which are modelled on the fusion in a Sylow p-subgroup of a finite group. It contains…
This is the third and last of three papers containing the complete proof that all finitely presented groups are QSF.
The notion of an internal preneighbourhood space on a finitely complete category with finite coproducts and a proper $(\mathsf{E}, \mathsf{M})$ system such that for each object $X$ the set of $\mathsf{M}$-subobjects of $X$ is a complete…
We classify the matrices M which correspond to finite categories
In this short note, we describe the finite groups $G$ having $|G|-1$ cyclic subgroups. This leads to a nice characterization of the symmetric group $S_3$.
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
A problem of constructing of local definitions for formations of finite groups is discussed in the article. The author analyzes relations between local definitions of various types. A new proof of existence of an $\omega$-composition…
Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.
This article is a sequel to hep-th/9411050, q-alg/9412017. In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number $\zeta$ an abelian artinian category $\FS$. We call its objects {\em finite…