#### 53 Citations

On the Kurosh theorem and separability properties

- Mathematics
- 2003

Abstract We prove a Kurosh-type subgroup theorem for free products of LERF groups. This theorem permits a better understanding of how finitely generated subgroups are embedded in finite index… Expand

Subgroup Into-Conjugacy Separability Property for Groups

- Mathematics
- 2012

Subgroup conjugacy separability ist eine Eigenschaft einer Gruppe, die logische Fortsetzung der folgenden Reihe von gut bekannten Gruppen- eigenschaften der Gruppen ist: residually ﬁniteness (RF),… Expand

Elementarily free groups are subgroup separable

- Mathematics
- 2005

Elementarily free groups are the finitely generated groups with the same elementary theory as free groups. We prove that elementarily free groups are subgroup separable, answering a question of Zlil… Expand

A Bass--Serre theoretic proof of a theorem of Burns and Romanovskii

- Mathematics
- 2021

A well known theorem of Burns and Romanovskii states that a free product of subgroup separable groups is itself subgroup separable. We provide a proof using the language of immersions and coverings… Expand

All finitely generated 3-manifold groups are Grothendieck rigid

- Mathematics
- 2021

In this paper, we prove that all finitely generated 3-manifold groups are Grothendieck rigid. More precisely, for any finitely generated 3manifold group G and any finitely generated proper subgroup H… Expand

Maximal subgroups and von Neumann subalgebras with the Haagerup property

- Mathematics
- Groups, Geometry, and Dynamics
- 2021

We initiate a study of maximal subgroups and maximal von Neumann subalgebras which have the Haagerup property. We determine maximal Haagerup subgroups inside $\mathbb{Z}^2 \rtimes SL_2(\mathbb{Z})$… Expand

Property (QT) of 3-manifold groups

- Mathematics
- 2021

Introduced by Bestvina-Bromberg-Fujiwara, a finitely generated group is said to have property (QT) if it acts isometrically on a finite product of quasi-trees so that orbital maps are quasi-isometric… Expand

On FC-central extensions of groups of intermediate growth

- Mathematics
- 2020

It is shown that FC-central extensions retain sub-exponential volume growth. A large collection of FC-central extensions of the first Grigorchuk group is provided by the constructions in the works of… Expand

Subgroup Separability of Artin Groups

- Mathematics
- 2020

We prove an Artin group is subgroup separable if and only if it can be obtained from the irreducible spherical Artin groups of rank 1 and 2 via a finite sequence of free products and direct products… Expand

A characterization on separable subgroups of 3‐manifold groups

- Mathematics
- Journal of Topology
- 2019

In this paper, we give a complete characterization on which finitely generated subgroups of finitely generated $3$-manifold groups are separable. Our characterization generalizes Liu's spirality… Expand

#### References

SHOWING 1-7 OF 7 REFERENCES

A note on free groups

- Mathematics
- 1969

The object of this note is to point out a theorem of M. Hall, Jr. (Theorem 1), proved, but formulated in a weaker form, as Theorem 5.1 of [2]. We then show that results of Karrass and Solitar [5],… Expand

On finitely generated subgroups of a free product

- Mathematics
- 1969

1. Introduction. In [2], M. Hall, Jr. proved the following theorem: Let 77 be a finitely generated subgroup of a free group Fand suppose ßi, • • • , ßn are in F but no ßi is in 77. Then we may… Expand

Schreier systems in free products

- Mathematics
- 1965

In 1927 Schreier [8] proved the Nielsen-Schreier Theorem that a subgroup H of a free group F is a free group by selecting a left transversal for H in F possessing a certain cancellation property.… Expand