The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Filters
On Products of Quasiconvex Subgroups in Hyperbolic Groups
[article]
2004
arXiv
pre-print
Preserved Fulltext
An interesting question about quasiconvexity in a hyperbolic group concerns finding classes of quasiconvex subsets that are closed under finite intersections. ...
In this work we study the properties of products of quasiconvex subgroups; we show that such sets are quasiconvex, their finite intersections have a similar algebraic representation and, thus, are quasiconvex ...
Therefore, a left coset of a quasiconvex subgroup and a conjugate subgroup to it are quasiconvex (in a hyperbolic group). Lemma 2.1. ...
arXiv:math/0404397v1
fatcat:zhtd4xifgng3fdcrjv3mfnz6ty
ON PRODUCTS OF QUASICONVEX SUBGROUPS IN HYPERBOLIC GROUPS
2004
International journal of algebra and computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Intersection of two quasiconvex subgroups of a hyperbolic group is, again, a quasiconvex subgroup. An important property of a hyperbolic group states that all its cyclic subgroups are quasiconvex. ...
Thus, all finite unions of ME-products constitute a topology T (of closed sets) on the set of elements of a hyperbolic group. ...
doi:10.1142/s0218196704001712
fatcat:afrbtk4rhvchvjgglqdvl6fg3y
Quasiconvexity and relatively hyperbolic groups that split
[article]
2012
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We then provide a criterion for the relative quasiconvexity of a subgroup H depending on the relative quasiconvexity of the intersection of H with the vertex groups of G. ...
We explore the combination theorem for a group G splitting as a graph of relatively hyperbolic groups. ...
Acknowledgement: We are extremely grateful to the anonymous f.g. referee whose very helpful corrections and adjustments improved the results and exposition of this paper. ...
arXiv:1211.1993v1
fatcat:qx3aa57mcbhobj6qyviwbzc7am
Separable subsets of GFERF negatively curved groups
2006
Journal of Algebra
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We show that in any such group, the product of finitely many quasiconvex subgroups is closed in the profinite topology on G. ...
A word hyperbolic group G is called GFERF if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it. ...
In particular, Gitik in [8, Theorem 1] proved that in a LERF hyperbolic group, a product of two quasiconvex subgroups, one of which is malnormal, is separable. ...
doi:10.1016/j.jalgebra.2006.03.050
fatcat:dibcuqczlnbgfmptidsxrxo5pm
Separable Subsets of GFERF Negatively Curved Groups
[article]
2006
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We show that in any such group, the product of finitely many quasiconvex subgroups is closed in the profinite topology on G. ...
A word hyperbolic group G is called GFERF if every quasiconvex subgroup coincides with the intersection of finite index subgroups containing it. ...
In particular, Gitik in [8, Thm. 1] proved that in a LERF hyperbolic group, a product of two quasiconvex subgroups, one of which is malnormal, is separable. ...
arXiv:math/0502101v2
fatcat:dmshxodwnnc53fqvh54dlu77lq
Detecting Relatively Quasiconvex Subgroups and Their Induced Peripheral Structure
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Other Versions
This paper proves under certain conditions the existence of an algorithm, which detects relatively quasiconvex subgroups H of relatively hyperbolic groups (G,ℙ). ...
Additionally, this algorithm outputs an induced peripheral structure of (G,ℙ) on H. ...
A natural class of subgroups of a relatively hyperbolic group (G, P) are the
relatively quasiconvex subgroups. ...
arXiv:2203.02357v2
fatcat:lvcdpfwz3zcexmhta3xzyx2tma
Virtual amalgamation of relatively quasiconvex subgroups
2012
Algebraic and Geometric Topology
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Other Versions
The main theorem extends results for quasiconvex subgroups of word-hyperbolic groups, and results for discrete subgroups of isometries of hyperbolic spaces. ...
For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups Q_1 and Q_2 is relatively quasiconvex and isomorphic to Q_1 ...
Acknowledgments We would like to thank Wen-yuan Yang for corrections on an earlier version of the paper, and for pointing out Corollary 6. ...
doi:10.2140/agt.2012.12.1993
fatcat:my5gxgfd2jeldkjeclluld5ndq
An example of a non-quasiconvex subgroup of a word hyperbolic group with exotic limit set
[article]
1995
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
In particular, this gives a counterexample to the conjecture of G.Swarup that a finitely presented one-ended subgroup of a word hyperbolic group is quasiconvex if and only if it has finite index in its ...
We construct an example of a torsion free freely indecomposable finitely presented non-quasiconvex subgroup H of a word hyperbolic group G such that the limit set of H is not the limit set of a quasiconvex ...
In this note we construct an example of a non-quasiconvex finitely presented one-ended subgroup H of a word hyperbolic group G such that the limit set of H is exotic. ...
arXiv:math/9506207v1
fatcat:fxez6q27nfcxxjw4trij6k2xuu
The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups
[article]
2012
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
We also study relations between relatively hyperbolic structures on a group and relative quasiconvexity for subgroups of the group. ...
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. ...
We also study relations between relatively hyperbolic structures on a group and relative quasiconvexity for subgroups of the group. ...
arXiv:1106.5288v3
fatcat:rdeihaqzmvhihkklxl3lpotd4e
On Quasiconvexity and Relative Hyperbolic Structures
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. ...
We characterize, for subgroups of G, when quasicovexity relative to A implies quasiconvexity relative to B. We also show that quasiconvexity relative to B implies quasiconvexity relative to A. ...
notion of quasiconvexity in word hyperbolic groups. ...
arXiv:0811.2384v4
fatcat:x4iqyhj5bbgw5lgeeejwwhtzay
On Residual Properties of Word Hyperbolic Groups
[article]
2006
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Other Versions
For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups. ...
Thus, a conjugate of a quasiconvex subgroup in a hyperbolic group is quasiconvex itself. ...
Free products of GFERF groups In the previous section we considered hyperbolic groups which engulf every proper quasiconvex subgroup. Let us name them QE-groups, for brevity. ...
arXiv:math/0506606v2
fatcat:wunfj2yuc5dfjbg3lp7vgw5ngm
On residual properties of word hyperbolic groups
2006
Journal of group theroy
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
For a fixed word hyperbolic group we compare different residual properties related to quasiconvex subgroups. 2000 Mathematics Subject Classification. Primary 20F67, Secondary 20E26. ...
Free products of GFERF groups In the previous section we considered hyperbolic groups which engulf every proper quasiconvex subgroup. Let us name them QE-groups, for brevity. ...
A hyperbolic group is called GFERF if each quasiconvex subgroup is closed in PT (G). ...
doi:10.1515/jgt.2006.045
fatcat:4k2osh3oznhs7euhnufvi3rdya
Subgroup properties of fully residually free groups
2001
Transactions of the American Mathematical Society
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We prove that fully residually free groups have the Howson property, that is the intersection of any two finitely generated subgroups in such a group is again finitely generated. ...
We also establish some commensurability properties for finitely generated fully residually free groups which are similar to those of free groups. ...
Infinite cyclic subgroups of word-hyperbolic groups are always quasiconvex [1] , so L is quasiconvex in A. ...
doi:10.1090/s0002-9947-01-02840-9
fatcat:xoqcsylhkfdqribmalc5ecf5py
Research announcement: The structure of groups with a quasiconvex hierarchy
2009
Electronic Research Announcements in Mathematical Sciences
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Let G be a word-hyperbolic group with a quasiconvex hierarchy. We show that G has a finite index subgroup G that embeds as a quasiconvex subgroup of a right-angled Artin group. ...
It follows that every quasiconvex subgroup of G is a virtual retract, and is hence separable. The results are applied to certain 3-manifold and one-relator groups. ...
The hierarchy terminates at a virtually free group of the form Z n * F . For one-relator groups with torsion, we show that the subgroups M, M are quasiconvex at each level of the hierarchy in [47] . ...
doi:10.3934/era.2009.16.44
fatcat:zhftsdi2wjf7vhwnilfasj6l5a
A non-quasiconvexity embedding theorem for hyperbolic groups
[article]
1997
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We show that if G is a non-elementary torsion-free word hyperbolic group then there exists another word hyperbolic group G^*, such that G is a subgroup of G^* but G is not quasiconvex in G^*. ...
Quasiconvex subgroups are of particularly great importance when one studies amalgamated free products and HNN-extensions of hyperbolic groups [Gr] , [BF1] , [KM] , [BGSS] , [Gi] , [Pa] . ...
Roughly speaking, a finitely generated subgroup H of a word hyperbolic group G is quasiconvex in G if for any word metric d G on G and any word metric d H on H the inclusion map i : (H, d H ) −→ (G, d ...
arXiv:math/9704203v1
fatcat:6gxhunx5wnawbj7ldlksa44jhu
« Previous
Showing results 1 — 15 out of 765 results