Related papers: Strong and uniform boundedness of groups

The nilpotent graph of a group $G$ is the simple and undirected graph whose vertices are the elements of $G$ and two distinct vertices are adjacent if they generate a nilpotent subgroup of $G$. Here we discuss some topological properties of…

An $integral$ of a group $G$ is a group $H$ whose derived group (commutator subgroup) is isomorphic to $G$. This paper discusses integrals of groups, and in particular questions about which groups have integrals and how big or small those…

For simple algebraic groups defined over algebraically closed fields of good characteristic, we give upper bounds on the covering numbers of unipotent conjugacy classes in terms of their (co)ranks and in terms of their dimensions.

We characterize the geometrically doubling condition of a metric space in terms of the uniform $L^1$-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.

Given a finite group $G$, the difference graph of $G$, denoted by $\mathcal{D}(G)$, is the difference of the enhanced power graph of $G$ and the power graph of $G$, with all isolated vertices removed. This paper mainly studies the…

$G$ be a finite group and $A$ a $G$-graded algebra over a field $F$ of characteristic zero. We characterize the varieties of $G$-graded algebras such that the multiplicities $m_{\langle \lambda \rangle}$ appering in the $\langle n \rangle…

Every semigroup containing an ideal subgroup is called a homogroup, and it is a grouplike if and only if it has only one central idempotent. On the other hand, a class of algebraic structures covering group-$e$-semigroups…

A group $G$ is said to have restricted centralizers if for every $x\in G$ the centralizer $C_G(x)$ either is finite or has finite index in $G$. Shalev showed that a profinite group with restricted centralizers is virtually abelian. Here we…

Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by…

If A is a finite dimensional nilpotent associative algebra over a finite field k, the set G=1+A of all formal expressions of the form 1+a, where a is an element of A, has a natural group structure, given by (1+a)(1+b)=1+(a+b+ab). A finite…

For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of…

Let $G$ be a Lie group acting on a vector space $V$. Given a set of $G$-invariants, one can ask the question : does this set of invariants characterize the group $G$ ? We recall here some known results, ask questions and state some…

Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…

Let $G$ be a primitive permutation group acting on a finite set $X$. The orbital diameter $\mathrm{diam}(X,G)$ is defined to be the supremum of the diameters of the (connected) orbital graphs of $G$ after disregarding the directions of all…

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

Let $G$ be a compact Lie group. Let ${\mathsf{F}}_n$ be the free group of rank $n$. We describe the orbits of ${\mathsf{Aut}}(\mathsf{F}_n)$ on ${\mathsf{Hom}}(\mathsf{F}_n;G)$ when $n$ is sufficiently large. The dynamics stabilizes: orbit…

In this paper, we show that the strong embeddability has fibering permanence property and is preserved under the direct limit for the metric space. Moreover, we show the following result: let $G$ is a finitely generated group with a coarse…

We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times…

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies to its possible homomorphisms into other…

Let $G$ be a locally compact group. If $G$ is finite then the amenability constant of its Fourier algebra, denoted by ${\rm AM}({\rm A}(G))$, admits an explicit formula [Johnson, JLMS 1994]; if $G$ is infinite then no such formula for ${\rm…