Stallings graphs, algebraic extensions and primitive elements in F 2

Ori Parzanchevski; Doron Puder

doi:https://doi.org/10.1017/S0305004114000097

Stallings graphs, algebraic extensions and primitive elements in F ²

Ori Parzanchevski, Doron Puder

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We study the free group of rank two from the point of view of Stallings core graphs. The first half of the paper examines primitive elements in this group, giving new and self-contained proofs for various known results about them. In particular, this includes the classification of bases of this group. The second half of the paper is devoted to constructing a counterexample to a conjecture by Miasnikov, Ventura and Weil, which seeks to characterize algebraic extensions in free groups in terms of Stallings graphs.

Original language	English
Pages (from-to)	1-11
Number of pages	11
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	157
Issue number	1
DOIs	https://doi.org/10.1017/S0305004114000097
State	Published - Jul 2014

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1017/S0305004114000097

Cite this

@article{996cd21c6c4946a498cbd127476d801c,

title = "Stallings graphs, algebraic extensions and primitive elements in F 2",

abstract = "We study the free group of rank two from the point of view of Stallings core graphs. The first half of the paper examines primitive elements in this group, giving new and self-contained proofs for various known results about them. In particular, this includes the classification of bases of this group. The second half of the paper is devoted to constructing a counterexample to a conjecture by Miasnikov, Ventura and Weil, which seeks to characterize algebraic extensions in free groups in terms of Stallings graphs.",

author = "Ori Parzanchevski and Doron Puder",

note = "Funding Information: Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by an Advanced ERC Grant. 07 2014 21 03 2014 157 1 1 11 11 12 2012 Copyright {\textcopyright} Cambridge Philosophical Society 2014 2014 Cambridge Philosophical Society Funding Information: Supported by an Advanced ERC Grant and the ISF.",

year = "2014",

month = jul,

doi = "https://doi.org/10.1017/S0305004114000097",

language = "الإنجليزيّة",

volume = "157",

pages = "1--11",

journal = "Mathematical Proceedings of the Cambridge Philosophical Society",

issn = "0305-0041",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Stallings graphs, algebraic extensions and primitive elements in F 2

AU - Parzanchevski, Ori

AU - Puder, Doron

N1 - Funding Information: Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by an Advanced ERC Grant. 07 2014 21 03 2014 157 1 1 11 11 12 2012 Copyright © Cambridge Philosophical Society 2014 2014 Cambridge Philosophical Society Funding Information: Supported by an Advanced ERC Grant and the ISF.

PY - 2014/7

Y1 - 2014/7

N2 - We study the free group of rank two from the point of view of Stallings core graphs. The first half of the paper examines primitive elements in this group, giving new and self-contained proofs for various known results about them. In particular, this includes the classification of bases of this group. The second half of the paper is devoted to constructing a counterexample to a conjecture by Miasnikov, Ventura and Weil, which seeks to characterize algebraic extensions in free groups in terms of Stallings graphs.

AB - We study the free group of rank two from the point of view of Stallings core graphs. The first half of the paper examines primitive elements in this group, giving new and self-contained proofs for various known results about them. In particular, this includes the classification of bases of this group. The second half of the paper is devoted to constructing a counterexample to a conjecture by Miasnikov, Ventura and Weil, which seeks to characterize algebraic extensions in free groups in terms of Stallings graphs.

UR - http://www.scopus.com/inward/record.url?scp=84901695588&partnerID=8YFLogxK

U2 - https://doi.org/10.1017/S0305004114000097

DO - https://doi.org/10.1017/S0305004114000097

M3 - مقالة

SN - 0305-0041

VL - 157

SP - 1

EP - 11

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 1

ER -

Stallings graphs, algebraic extensions and primitive elements in F ²

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this