Related papers: Abelian subgroups of Garside groups

Let p be an odd prime. The lattice of all normal subgroups and the terms of the lower and upper central series are determined for all metabelian p-groups with generator rank d=2 having abelianization of type (p,p) and minimal defect of…

This paper is concerned with absolutely irreducible quasisimple subgroups $G$ of a finite general linear group $GL_d(\mathbb{F}_q)$ for which some element $g\in G$ of prime order $r$, in its action on the natural module…

Let $\mathbf G$ be a connected reductive algebraic group over an algebraically closed field, and let $s\in\mathbf G$ be a semisimple element. We show that the centraliser of $s$ is the semi-direct product of its identity component by its…

In "A note on generalized Clifford algebras and representations" (Caenepeel, S.; Van Oystaeyen, F., Comm. Algebra 17 (1989) no. 1, 93--102.) generalized Clifford algebras were introduced via Clifford representations; these correspond to…

For a homogeneous space X of a connected algebraic group G (with connected stabilizers) over a field k of characteristic zero, we construct a canonical complex of Galois modules of length 3 and a canonical isomorphism between an…

withdrawn and included in our new manuscript "Abelian subgroups of Garside groups", math.GT/0609683

Let G be a reductive group over a commutative ring R. We say that G has isotropic rank >=n, if every normal semisimple reductive R-subgroup of G contains (G_m)^n. We prove that if G has isotropic rank >=1 and R is a regular domain…

Given a connected linear algebraic group $G$, we descrive the subgroup of $G$ generated by all semisimple elements.

Let $\mathfrak{g}$ be a simple Lie algebra of exceptional type over an algebraically closed field $k$, and let $G$ be a simple linear algebraic group with Lie algebra $\mathfrak{g}$. For $\mathrm{char} \, k =p >0$, we present a complete…

We complete the study of finite and profinite groups admitting an action by an elementary abelian group under which the centralizers of automorphisms consist of Engel elements. In particular, we prove the following theorems. Let $q$ be a…

Let G be the pro-algebraic group attached to the tannakian category of polarizable rational Hodge structures. We show that the quotient of G by its derived group is the Serre group, the derived group of G is the simply connected covering of…

Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This…

For a group $G$, let $U$ be the group of units of the integral group ring $\mathbb{Z}G$. The group $G$ is said to have the normalizer property if $\text{N}_U(G)=\text{Z}(U)G$. It is shown that Blackburn groups have the normalizer property.…

In the study of the local dynamics of a germ of diffeomorphism fixing the origin in C, an important problem is to determine the centralizer of the germ in the group Diff(C,0) of germs of diffeomorphisms fixing the origin. When the germ is…

We study the centralizer of a braid from the point of view of Garside theory, showing that generically a minimal set of generators can be computed very efficiently, as the ultra summit set of a generic braid has a very particular structure.…

It is known that Garside groups are strongly translation discrete. In this paper, we show that the translation numbers in a Garside group are rational with uniformly bounded denominators and can be computed in finite time. As an…

Let $G$ be a simple algebraic group of type $A$ or $D$ defined over $\C$ and $T$ be a maximal torus of $G$. For a dominant coweight $\lambda$ of $G$, the $T$-fixed point subscheme $(\bar{Gr}_G^\lambda)^T$ of the Schubert variety…

A paratopological group $G$ is saturated if the inverse $U^{-1}$ of each non-empty set $U\subset G$ has non-empty interior. It is shown that a [first-countable] paratopological group $H$ is a closed subgroup of a saturated (totally bounded)…

Let G be a reductive linear algebraic group over an algebraically closed field of characteristic p > 0. A subgroup of G is said to be separable in G if its global and infinitesimal centralizers have the same dimension. We study the…

An Engel sink of an element $g$ of a group $G$ is a set ${\mathscr E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$. (Thus, $g$ is an Engel element precisely when we…