Related papers: Isogeny in Superstable Groups
We consider an inhomogeneous quantum supergroup which leaves invariant a supersymmetric particle algebra. The quantum sub-supergroups of this inhomogeneous quantum supergroup are investigated.
We develop local stable group theory directly from topological dynamics, and extend the main results in this subject to the setting of stability "in a model". Specifically, given a group $G$, we analyze the structure of sets $A\subseteq G$…
Let T be a rooted tree and Iso(T) be the group of isometries of T. Using model-theoretic tools we study closed subgroups G of Iso(T) with respect to the number of conjugacy classes of Iso(T) having representatives in G.
We study adequate subgroups of $GL_n$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to be adequate.
We exhibit a simple condition under which a finite involutary semigroup whose semigroup reduct is inherently nonfinitely based is also inherently nonfinitely based as a unary semigroup. As applications, we get already known as well as new…
The concept of configuration was first introduced by Rosenblatt and Willis to give a characterization for the amenability of groups. We show that group properties of being soluble or FC can be characterized by configuration sets. Then we…
We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show…
In this work we employ machine learning to understand structured mathematical data involving finite groups and derive a theorem about necessary properties of generators of finite simple groups. We create a database of all 2-generated…
The stability of ecological systems is a fundamental concept in ecology, which offers profound insights into species coexistence, biodiversity, and community persistence. In this article, we provide a systematic and comprehensive review on…
A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…
A review of the superstatistics concept is provided, including various recent applications to complex systems.
We prove the so-called Unitary Isotropy Theorem, a result on isotropy of a unitary involution. The analogous previously known results on isotropy of orthogonal and symplectic involutions as well as on hyperbolicity of orthogonal,…
We consider the Vlasov-Poisson system in a cosmological setting and prove nonlinear stability of homogeneous solutions against small, spatially periodic perturbations in the sup-norm of the spatial mass density. This result is connected…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
A group $G$ is invariably generated (IG) if there is a subset $S \subseteq G$ such that for every subset $S' \subseteq G$, obtained from $S$ by replacing each element with a conjugate, $S'$ generates $G$. $G$ is finitely invariably…
We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…
We formulate a new criterion of the asymptotic stability for some non-equicontinuous Markov semigroups, the so-called eventually continuous semigroups. In particular, we provide a non-equicontinuous Markov semigroup example with essential…
A new approach to superstability and finite time extinction of strongly continuous semigroups is presented, unifying known results and providing new criteria for these conditions to hold analogous to the well-known Pazy condition for…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.