Related papers: Breaking points in centralizer lattices
Let $G$ be a finite non-solvable group with solvable radical $Sol(G)$. The solvable graph $\Gamma_s(G)$ of $G$ is a graph with vertex set $G\setminus Sol(G)$ and two distinct vertices $u$ and $v$ are adjacent if and only if $\langle u, v…
The classification of flag-transitive generalised quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory. Given that all known flag-transitive generalised quadrangles are also…
The Lorentz invariant $CPT$ violation by using non-local interactions is naturally incorporated in the Higgs coupling to neutrinos in the Standard Model, without spoiling the basic $SU(2)_{L}\times U(1)$ gauge symmetry. The…
Let $G$ be a finite group. Let $\mathcal{N}(G)$ be the lattice of normal subgroups ordered by inclusion, regarded as an abstract lattice. Define $\operatorname{LatAut}(G) := \operatorname{Aut}(\mathcal{N}(G))$. The \emph{LatAut tower} is…
We study the dynamics of SU(2) gauge theory with NF=6 Dirac fermions by means of lattice simulation to investigate if they are appropriate to realization of electroweak symmetry breaking. The discrete analogue of beta function for the…
How far can the elementary description of centralizers of parabolic subalgebras of Hecke algebras of finite real reflection groups be generalized to the complex reflection group case? In this paper we begin to answer this question by…
Let G be any locally compact, unimodular, metrizable group. The main result of this paper, roughly stated, is that if F<G is any finitely generated free group and \Gamma < G any lattice, then up to a small perturbation and passing to a…
Suppose that a locally finite group $G$ has a $2$-element $g$ with Chernikov centralizer. It is proved that if the involution in $\langle g\rangle$ has nilpotent centralizer, then $G$ has a soluble subgroup of finite index.
Let $\mathfrak A_n$ be the subset of the standard integer lattice $\mathbb Z^n$, $\mathfrak A_n\subset\mathbb Z^n$ which is defined by the condition $\mathfrak A_n=((a_1,...,a_n)\in\mathbb Z^n | a_i\not\equiv a_j\mod n, \forall i,j\in…
We suggest a tetracritical fixed point to naturally occur in strongly interacting theories. As a fundamental example we analyze the temperature--quark chemical potential phase diagram of QCD with fermions in the adjoint representation of…
We show that for any $\alpha\in (1/2,1)$ the number of lattice points belonging to an arc of length $R^{\alpha}$ of the circle of radius $R$ centered at the origin is not uniformly bounded in $R$, which disproves the corresponding…
We discuss the mediation of supersymmetry breaking from closed to open strings, extending and improving previous analysis of the authors in Nucl. Phys. B 695 (2004) 103 [hep-th/0403293]. In the general case, we find the absence of anomaly…
Let $G$ be a connected Lie group and $\Gamma \subset G$ a lattice. Connection curves of the homogeneous space $M=G/\Gamma$ are the orbits of one parameter subgroups of $G$. To \textit{block} a pair of points $m_1,m_2 \in M$ is to find a…
We investigate the phase structure of lattice QCD for general number of flavors $N_F$. Based on numerical results combined with the result of the perturbation theory we propose the following picture: When $N_F \ge 17$, there is only a…
For a given m>=1, we consider the finite non-abelian groups G for which |C_G(g):<g>|<=m for every g in G\Z(G). We show that the order of G can be bounded in terms of m and the largest prime divisor of the order of G. Our approach relies on…
A finite group $G$ is a CG-group if $|{\rm Cent}(G) | = | G' |+2$, where $G'$ is the commutator subgroup and Cent$(G)$ is the set of distinct element centralizers of $G$. In this paper we give some results on CG-groups. We also give a…
Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the…
The Congruence Lattice Problem (CLP), stated by R. P. Dilworth in the forties, asks whether every distributive {∨, 0}-semilatticeS is isomorphic to the semilattice Conc L of compact congruences of a lattice L. While this problem is…
Let $G$ be a right-angled Artin group with defining graph $\Gamma$ and let $H$ be a finitely generated group quasi-isometric to $G(\Gamma)$. We show if $G$ satisfies (1) its outer automorphism group is finite; (2) $\Gamma$ does not have…
We investigate the representation of lattices as sublattices of the lattice of all convex subsets (intervals) of a linearly ordered set $(X,\le)$. We introduce the purely lattice-theoretic notion of a \textit{loc-lattice} and prove that…