1997
DOI: 10.1006/jabr.1996.6847
|View full text |Cite
|
Sign up to set email alerts
|

Graphs and Separability Properties of Groups

Abstract: Ž. A group G is LERF locally extended residually finite if for any finitely generated subgroup S of G and for any g f S there exists a finite index subgroup S of G which contains S but not g. Using graph-theoretical methods we give 0 algorithms for constructing finite index subgroups in amalgamated free products of groups with good separability properties. We prove that a free product of a free group and a LERF group amalgamated over a cyclic subgroup maximal in the free factor is LERF. The maximality conditio… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
52
0

Year Published

2001
2001
2017
2017

Publication Types

Select...
5
2

Relationship

0
7

Authors

Journals

citations
Cited by 34 publications
(52 citation statements)
references
References 17 publications
0
52
0
Order By: Relevance
“…Three general theorems have been proved about subgroup separability of graphs of groups. One concerns the amalgamation of a subgroup separable group and a free group [6]. Another concerns graphs of free groups [33].…”
Section: The Motivating Ideamentioning
confidence: 99%
See 2 more Smart Citations
“…Three general theorems have been proved about subgroup separability of graphs of groups. One concerns the amalgamation of a subgroup separable group and a free group [6]. Another concerns graphs of free groups [33].…”
Section: The Motivating Ideamentioning
confidence: 99%
“…In [6], Gitik uses a notion of pre-cover; our pre-covers are analogous to hers.ΓΓ Figure 2: The diagram shows the covering spaceΓ from Figure 1. A finite subgraphΓ ofΓ is drawn with a thick line.…”
Section: Pre-coversmentioning
confidence: 99%
See 1 more Smart Citation
“…Similar techniques are used by Gitik [48], [49] to study separability properties and quasiconvexity in hyperbolic groups and by Steinberg [135], [136], [137] to study monoid presentations and profinite topologies on free groups. Methods related to Stallings foldings, making use of 2-complexes instead of graphs, have been employed by McCammond and Wise [97] to study coherence in groups and by Schupp [127] to study surface groups and Coxeter groups of extra large type.…”
Section: Theorem 14 Letmentioning
confidence: 99%
“…Since then many people have worked on the subject. For the families of groups that are known to satisfy subgroup separability the reader should consult the papers of Gitik [8] and Wise [19] and the references cited there.…”
Section: Introductionmentioning
confidence: 99%