scholarly journals Virtual amalgamation of relatively quasiconvex subgroups

2012 ◽  
Vol 12 (4) ◽  
pp. 1993-2002 ◽  
Author(s):  
Eduardo Martínez-Pedroza ◽  
Alessandro Sisto
Keyword(s):  
Quasiconvex Subgroups

scholarly journals Notes on Relatively Hyperbolic Groups and Relatively Quasiconvex Subgroups

2015 ◽  
Vol 38 (1) ◽  
pp. 99-123
Author(s):  
Yoshifumi MATSUDA ◽  
Shin-ichi OGUNI ◽  
Saeko YAMAGATA
Keyword(s):  
Hyperbolic Groups ◽  
Relatively Hyperbolic Groups ◽  
Quasiconvex Subgroups ◽  
Relatively Hyperbolic

scholarly journals ON PRODUCTS OF QUASICONVEX SUBGROUPS IN HYPERBOLIC GROUPS

2004 ◽  
Vol 14 (02) ◽  
pp. 173-195 ◽  
Author(s):  
ASHOT MINASYAN
Keyword(s):  
Hyperbolic Group ◽  
Hyperbolic Groups ◽  
Algebraic Representation ◽  
Quasiconvex Subgroups

An interesting question about quasiconvexity in a hyperbolic group concerns finding classes of quasiconvex subsets that are closed under finite intersections. A known example is the class of all quasiconvex subgroups [1]. However, not much is yet learned about the structure of arbitrary quasiconvex subsets. In this work we study the properties of products of quasiconvex subgroups; we show that such sets are quasiconvex and their finite intersections have a similar algebraic representation and, thus, are quasiconvex too.

scholarly journals Quasiconvex subgroups of negatively curved groups

1994 ◽  
Vol 95 (3) ◽  
pp. 297-301 ◽  
Author(s):  
Michael L. Mihalik ◽  
Williams Towle
Keyword(s):  
Negatively Curved ◽  
Quasiconvex Subgroups

scholarly journals Growth of quasiconvex subgroups

2018 ◽  
Vol 167 (3) ◽  
pp. 505-530 ◽  
Author(s):  
FRANÇOIS DAHMANI ◽  
DAVID FUTER ◽  
DANIEL T. WISE
Keyword(s):  
Hyperbolic Groups ◽  
Infinite Index ◽  
Relatively Hyperbolic Groups ◽  
Automatic Structures ◽  
Quasiconvex Subgroups ◽  
Relatively Hyperbolic

AbstractWe prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron–Frobenius theory.We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions use the notion of growth tightness and the work of Dahmani, Guirardel and Osin on rotating families.

On intersections of conjugate subgroups

2017 ◽  
Vol 27 (04) ◽  
pp. 403-419 ◽  
Author(s):  
Rita Gitik
Keyword(s):  
Conjugacy Class ◽  
Generating Set ◽  
Explicit Algorithm ◽  
Negatively Curved ◽  
Coset Graph ◽  
Finite Breadth ◽  
Quasiconvex Subgroups

We define a new invariant of a conjugacy class of subgroups which we call the breadth and prove that a quasiconvex subgroup of a negatively curved group has finite breadth in the ambient group. Utilizing the coset graph and the geodesic core of a subgroup we give an explicit algorithm for constructing a finite generating set for an intersection of a quasiconvex subgroup of a negatively curved group with its conjugate. Using that algorithm we construct algorithms for computing the breadth, the width, and the height of a quasiconvex subgroup of a negatively curved group. These algorithms decide if a quasiconvex subgroup of a negatively curved group is almost malnormal in the ambient group. We also explicitly compute a quasiconvexity constant of the intersection of two quasiconvex subgroups and give examples demonstrating that height, width, and breadth are different invariants of a subgroup.

On convex hulls and the quasiconvex subgroups of Fm×ℤn

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Jordan Sahattchieve
Keyword(s):  
Convex Hull ◽  
Metric Space ◽  
Convex Hulls ◽  
Geodesic Metric Space ◽  
Geodesic Metric ◽  
Quasiconvex Subgroups

AbstractIn this paper, we explore a method for forming the convex hull of a subset in a uniquely geodesic metric space due to Brunn and use it to show that with respect to the usual action of

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