Related papers: Goursat completions
We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
In this paper we introduce and study the concept of normality degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be normal. Explicit formulas are obtained for some particular classes of…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is achieved.
We study locally presentable categories equipped with a cofibrantly generated weak factorization system. Our main result is that these categories are closed under 2-limits, in particular under pseudopullbacks. We give applications to…
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…
In order to diagnose the cause of some defects in the category of canonical hypergroups, we investigate several categories of hyperstructures that generalize hypergroups. By allowing hyperoperations with possibly empty products, one obtains…
We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…
Gowers has elegantly characterized the finite groups $G$ in which $A_1A_2A_3 = G$ for any positive density subsets $A_1,A_2,A_3$. This property, quasi-randomness, holds if and only if G does not admit a nontrivial irreducible representation…
In this note we prove that additive categories that occur as hearts of weight structures are precisely the weakly idempotent completecategories, that is, the categories where all split monomorphisms give direct sum decompositions. We also…
We prove that a certain conjecture holds true and the conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.
We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
Let $ x $ be an element of a finite group $ G $ and denote the order of $ x $ by $ \mathrm{ord}(x) $. We consider a finite group $ G $ such that $ \gcd(\mathrm{ord}(x),\mathrm{ord}(y))\leqslant 2 $ for any two vanishing elements $ x $ and $…
This article introduces Hilbert $*$-categories: an abstraction of categories with similar algebraic and analytic properties to the categories of real, complex, and quaternionic Hilbert spaces and bounded linear maps. Other examples include…
Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In…
We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…
Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are…