Membership Problem in groups acting freely on Zn-trees

Andrey Nikolaev; Denis Serbin

doi:10.1016/j.jalgebra.2012.07.038

Membership Problem in groups acting freely on Zn-trees

Andrey Nikolaev
, Denis Serbin

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Groups acting freely on Zn-trees (Zn-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to investigate subgroup structure of Zn-free groups. As an immediate application of the presented method, we give an effective solution to the Uniform Membership Problem and the Power Problem in Zn-free groups.

Original language	English
Pages (from-to)	410-444
Number of pages	35
Journal	Journal of Algebra
Volume	370
DOIs	https://doi.org/10.1016/j.jalgebra.2012.07.038
State	Published - 15 Nov 2012

Keywords

Group actions
Membership Problem
Zn-trees

Access to Document

10.1016/j.jalgebra.2012.07.038

Cite this

@article{397eea878eed4fd990f4dfcf71667e42,

title = "Membership Problem in groups acting freely on Zn-trees",

abstract = "Groups acting freely on Zn-trees (Zn-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to investigate subgroup structure of Zn-free groups. As an immediate application of the presented method, we give an effective solution to the Uniform Membership Problem and the Power Problem in Zn-free groups.",

keywords = "Group actions, Membership Problem, Zn-trees",

author = "Andrey Nikolaev and Denis Serbin",

year = "2012",

month = nov,

day = "15",

doi = "10.1016/j.jalgebra.2012.07.038",

language = "English",

volume = "370",

pages = "410--444",

}

TY - JOUR

T1 - Membership Problem in groups acting freely on Zn-trees

AU - Nikolaev, Andrey

AU - Serbin, Denis

PY - 2012/11/15

Y1 - 2012/11/15

N2 - Groups acting freely on Zn-trees (Zn-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to investigate subgroup structure of Zn-free groups. As an immediate application of the presented method, we give an effective solution to the Uniform Membership Problem and the Power Problem in Zn-free groups.

AB - Groups acting freely on Zn-trees (Zn-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to investigate subgroup structure of Zn-free groups. As an immediate application of the presented method, we give an effective solution to the Uniform Membership Problem and the Power Problem in Zn-free groups.

KW - Group actions

KW - Membership Problem

KW - Zn-trees

UR - https://www.scopus.com/pages/publications/84865967187

UR - https://www.scopus.com/pages/publications/84865967187#tab=citedBy

U2 - 10.1016/j.jalgebra.2012.07.038

DO - 10.1016/j.jalgebra.2012.07.038

M3 - Article

AN - SCOPUS:84865967187

SN - 0021-8693

VL - 370

SP - 410

EP - 444

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Membership Problem in groups acting freely on Zn-trees

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this