Search results for "combinatoric"
showing 10 items of 1776 documents
The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group
2000
It was conjectured by Tits that the only relations amongst the squares of the standard generators of an Artin group are the obvious ones, namely that a^2 and b^2 commute if ab=ba appears as one of the Artin relations. In this paper we prove Tits' conjecture for all Artin groups. More generally, we show that, given a number m(s)>1 for each Artin generator s, the only relations amongst the powers s^m(s) of the generators are that a^m(a) and b^m(b) commute if ab=ba appears amongst the Artin relations.
The conjugacy problem in subgroups of right-angled Artin groups
2009
We prove that the conjugacy problem in right-angled Artin groups (RAAGs), as well as in a large and natural class of subgroups of RAAGs, can be solved in linear-time. This class of subgroups contains, for instance, all graph braid groups (i.e. fundamental groups of configuration spaces of points in graphs), many hyperbolic groups, and it coincides with the class of fundamental groups of ``special cube complexes'' studied independently by Haglund and Wise.
A Local Approach to Certain Classes of Finite Groups
2003
Abstract We develop several local approaches for the three classes of finite groups: T-groups (normality is a transitive relation) and PT-groups (permutability is a transitive relation) and PST-groups (S-permutability is a transitive relation). Here a subgroup of a finite group G is S-permutable if it permutes with all the Sylow subgroup of G.
Commensurators of parabolic subgroups of Coxeter groups
1996
Let $(W,S)$ be a Coxeter system, and let $X$ be a subset of $S$. The subgroup of $W$ generated by $X$ is denoted by $W_X$ and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the commensurator of $W_X$ in $W$ is the subgroup of $w$ in $W$ such that $wW_Xw^{-1}\cap W_X$ has finite index in both $W_X$ and $wW_Xw^{-1}$. The subgroup $W_X$ can be decomposed in the form $W_X = W_{X^0} \cdot W_{X^\infty} \simeq W_{X^0} \times W_{X^\infty}$ where $W_{X^0}$ is finite and all the irreducible components of $W_{X^\infty}$" > are infinite. Let $Y^\infty$ be the set of $t$ in $S$ such that $m_{s,t}=2$" > for all $s\in X^\i…
The case of equality in the dichotomy of Mohammadi–Oh
2019
If $n \geq 3$ and $\Gamma$ is a convex-cocompact Zariski-dense discrete subgroup of $\mathbf{SO}^o(1,n+1)$ such that $\delta_\Gamma=n-m$ where $m$ is an integer, $1 \leq m \leq n-1$, we show that for any $m$-dimensional subgroup $U$ in the horospheric group $N$, the Burger-Roblin measure associated to $\Gamma$ on the quotient of the frame bundle is $U$-recurrent.
Symbolic Dynamics of Geodesic Flows on Trees
2019
In this chapter, we give a coding of the discrete-time geodesic ow on the nonwandering sets of quotients of locally finite simplicial trees X without terminal vertices by nonelementary discrete subgroups of Aut(X) by a subshift of finite type on a countable alphabet.
Nilpotent length and system permutability
2022
Abstract If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschutz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible.
Nilpotent-like fitting formations of finite soluble groups
2000
[EN] In this paper the subnormal subgroup closed saturated formations of finite soluble groups containing nilpotent groups are fully characterised by means of extensions of well-known properties enjoyed by the formation of all nilpotent groups.
Generalised norms in finite soluble groups
2014
Abstract We give a framework for a number of generalisations of Baerʼs norm that have appeared recently. For a class C of finite nilpotent groups we define the C -norm κ C ( G ) of a finite group G to be the intersection of the normalisers of the subgroups of G that are not in C . We show that those groups for which the C -norm is not hypercentral have a very restricted structure. The non-nilpotent groups G for which G = κ C ( G ) have been classified for some classes. We give a classification for nilpotent classes closed under subgroups, quotients and direct products of groups of coprime order and show the known classifications can be deduced from our classification.
Explicit Measure Computations for Simplicial Trees and Graphs of Groups
2019
In this chapter, we compute skinning measures and Bowen{Margulis measures for some highly symmetric simplicial trees X endowed with a nonelementary discrete subgroup Г of Aut(X).