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We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Consider the expansion $T_S$ of a theory $T$ by a predicate for a submodel of a reduct $T_0$ of $T$. We present a setup in which this expansion admits a model companion $TS$. We show that the nice features of the theory $T$ transfer to…
Let K be an algebraically bounded structure and T be its theory. If T is model complete, then the theory of K endowed with a derivation, denoted by $T^{\delta}$, has a model completion. Additionally, we prove that if the theory T is…
In this paper, we provide several instances in which interesting approximation and stability properties are inherited by quotients with respect to finitely generated normal subgroups or, more strongly, normal subgroups with Kazhdan's…
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…
It is known that the notion of a transitive subgroup of a permutation group $G$ extends naturally to subsets of $G$. We consider subsets of the general linear group $\operatorname{GL}(n,q)$ acting transitively on flag-like structures, which…
The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…
Let $G$ be a finite group. We study the generalized character defined by $\Xi(g)=|G|o(g)$, for $g\in G$, which is closely related to a function that has been very studied recently from a group theoretical point of view.
We generalize Philip Hall's celebrated theorems on finite solvable groups to scheme theory. Our result is based on a series of results on hypergroups.
In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
In this paper we continue Prasma's homotopical group theory program by considering homotopy normal maps in arbitrary $\infty$-topoi. We show that maps of group objects equipped with normality data, in Prasma's sense, are algebras for a…
In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.
We give a simple generalisation of a theorem of Morita, which leads to a great number of relations among tautological classes on moduli spaces of curves.
The characterization of normal subgroups M, N of free group F for which the quotient group F/[M,N] is finitely presented is given.
Let $(X, \sigma)$ be a transitive sofic shift and let $\rm{Aut}(X)$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\rm{Aut}(X)$ must be contained in the…
We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams systems for the corresponding topological objects. We will…
We consider Turing machines as actions over configurations in $\Sigma^{\mathbb{Z}^d}$ which only change them locally around a marked position that can move and carry a particular state. In this setting we study the monoid of Turing machines…
A valuated group with normal forms is a group with an integer-valued length function satisfying some Lyndon's axioms and an additional axiom considered by Hurley. We prove a subgroup theorem for valuated groups with normal forms analogous…