Related papers: Locally Finite Root Supersystems
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.
Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.
We introduce the notion of soficity for locally compact groups and list a number of open problems.
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the…
We study cofinal systems of finite subsets of $\omega_1$. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: in an NIP theory,…
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.
We point out a connection between root systems and some of the known hyperk\"ahler varieties.
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 introduce the notion of unbounded locally solid Riesz spaces, and investigate its fundamental properties.
The structure of Lie algebras, Lie superalgebras and Leibniz algebras graded by finite root systems has been studied by several researchers since 1992. In this paper, we study the structure of Leibniz superalgebras graded by finite root…
Locally finite groups having the property that every non-cyclic subgroup contains its centralizer are completely classified.
We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.
Tree sets are posets with additional structure that generalize tree-like objects in graphs, matroids, or other combinatorial structures. They are a special class of abstract separation systems. We study infinite tree sets and how they…
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…
The concept of an omnigenous locally finite group was introduced in [2] as a generalization of Hall's universal countable locally finite group. In this paper we show that the class of all countable omnigenous locally finite groups is Borel…
We develop structure theory of finite Lie conformal superalgebras.
We consider groups of finite Morley rank with solvable local subgroups of even and mixed types. We also consider miscellaneous aspects of small groups of finite Morley rank of odd type.
Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between angles and sums and differences of elements. They conjecture…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
We determine the finite groups whose real irreducible representations have different degrees.