Related papers: Engel Elements in Groups
In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.
In this paper we study powerful 3-Engel groups. In particular, we find sharp upper bounds for the nilpotency class of powerful 3-Engel groups and the subclass of powerful metabelian 3-Engel groups.
The main result of this paper states that for any group $G$ with an automatic structure $L$ with unique representatives one can construct a uniform partial algorithm which detects $L$-rational subgroups and gives their preimages in $L$.…
We give a comprehensive study of the so-called \textit{semi-tripotent rings} obtaining their new and non-trivial characterization as well as a complete description in terms of sums and products of some special elements. Particularly, we…
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.
Let G be a linear group such that for every g in G there is a finite set R(g) with the property that for every x in G all sufficiently long commutators [g,x,x,...,x] belong to R(g). It is proved that G is finite-by-hypercentral.
In this note some properties of the sum of element orders of a finite abelian group are studied.
We call two Engel structures isotopic if they are homotopic through Engel structures by a homotopy that fixes the characteristic line field. In the present paper we define an isotopy invariant of Engel structures on oriented circle bundles…
A survey article that presents some recent algebraic and model-theoretic results on the automorphism groups of relatively free groups of infinite rank. The topics include topological aspects, generating sets, descripition of automorpisms…
This paper discusses the left and right ranks of quaternion matrices with Hankel structure. While they are in general different for arbitrary quaternion matrices, we show that the left and right ranks of quaternion Hankel matrices are…
We explore to what extent the underlying variety of a connected algebraic group or the underlying manifold of a real Lie group determines its group structure.
Clustering and community structure is crucial for many network systems and the related dynamic processes. It has been shown that communities are usually overlapping and hierarchical. However, previous methods investigate these two…
In this article we survey some of the recent developments in the structure theory of set addition.
A (left) Engel sink of an element g of a group G is a subset containing all sufficiently long commutators [...[[x,g],g],...,g], where x ranges over G. We prove that if p is a prime and G a finite group in which, for some positive integer m,…
We define a class of quandle-like structures called pseudoquandles and analyze some of their algebraic properties.
This is a survey on left invariant semi-Riemannian metrics on compact Lie groups.
We present a self-contained analysis of infinity from two mathematical perspectives: set theory and algebra. We begin with cardinal and ordinal numbers, examining deep questions such as the continuum hypothesis, along with foundational…
We introduce an algebraic framework for the description of baryons. Within this framework we study a collective string-like model and show that this model gives a good overall description of the presently available data. We discuss in…
An element $g$ in a group $G$ is called \emph{reciprocal} if there exists $h \in G$ such that $g^{-1}=hgh^{-1}$. The reciprocal elements are also known as `real elements' or `reversible elements' in the literature. We classify the…
We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.