Results 21 to 30 of about 354,932 (255)
On knot groups acting on trees
Journal of Knot Theory and Its Ramifications, 2020 A finitely generated group [Formula: see text] acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag–Solitar group (GBS group). We prove that a one-knot group [Formula: see text] is a GBS group if and only if [Formula: see text] is a torus knot group, and describe all n-knot GBS groups for [Formula: see ...
Fedor A. Dudkin, Andrey S. Mamontov
openaire +3 more sources
On invertor elements and finitely generated subgroups of groups acting on trees with inversions
International Journal of Mathematics and Mathematical Sciences, 2000 An element of a group acting on a graph is called invertor if it transfers an edge of the graph to its inverse. In this paper, we show that if G is a group acting on a tree X with inversions such that G does not fix any element of X, then an element g of
R. M. S. Mahmood, M. I. Khanfar
doaj +1 more source
International Journal of Mathematics and Mathematical Sciences, 2002 We extend the structure theorem for the subgroups of the class of HNN groups to a new class of groups called quasi-HNN groups. The main technique used is the subgroup theorem for groups acting on trees with inversions.
R. M. S. Mahmood, M. I. Khanfar
doaj +1 more source
GROUPS ACTING ON TREES WITH PRESCRIBED LOCAL ACTION
Journal of the Australian Mathematical Society, 2022 AbstractWe extend the Burger–Mozes theory of closed, nondiscrete, locally quasiprimitive automorphism groups of locally finite, connected graphs to the semiprimitive case, and develop a generalization of Burger–Mozes universal groups acting on the regular tree $T_{d}$ of degree $d\in \mathbb {N}_{\ge 3}$ . Three applications are given.
openaire +3 more sources
On the Positive Theory of Groups Acting on Trees [PDF]
International Mathematics Research Notices, 2020 Abstract In this paper, we study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, that is, coincides with the positive theory of a non-abelian free group.
Casals-Ruiz, Montserrat +2 more
openaire +2 more sources
New examples of groups acting on real trees
, 2015 We construct the first example of a finitely generated group which has Serre's property (FA) (i.e., whenever it acts on a simplicial tree it fixes a vertex), but admits a fixed point-free action on an $\mathbb{R}$-tree with finite arc stabilizers.
Minasyan, Ashot
core +1 more source
Scientia Agricola, 2010 Ecological theories of facilitation and nucleation are proposed as a basis for environmental restoration in tropical ecosystems. The main goal of this paper is to present restoration techniques based on the concept of nucleation, in which small nuclei of
Ademir Reis +2 more
doaj +1 more source
Zeta Functions of Discrete Groups Acting on Trees
Journal of Algebra, 2001 This paper generalizes Bass' work on zeta functions for uniform tree lattices. Using the theory of von Neumann algebras, machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree. The main theorems relate the zeta function to determinants of operators defined on edges or vertices of the tree.
Clair, Bryan, Mokhtari-Sharghi, Shahriar
openaire +2 more sources
Highly transitive actions of groups acting on trees [PDF]
Proceedings of the American Mathematical Society, 2015 We show that a group acting on a non-trivial tree with finite edge stabilizers and icc vertex stabilizers admits a faithful and highly transitive action on an infinite countable set. This result is actually true for infinite vertex stabilizers and some more general, finite of infinite, edge stabilizers that we call highly core-free. We study the notion
Fima, Pierre +2 more
openaire +4 more sources
Groups acting on trees with almost prescribed local action
, 2016 We investigate a family of groups acting on a regular tree, defined by prescribing the local action almost everywhere. We study lattices in these groups and give examples of compactly generated simple groups of finite asymptotic dimension (actually one ...
Boudec, Adrien Le
core +1 more source