Embedding ℤ2 * Z as a discrete subgroup into small linear groups

G. A. Soifer

doi:10.1142/S0218196712500579

Embedding ℤ² * Z as a discrete subgroup into small linear groups

G. A. Soifer

Department of Mathematics

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

1 Scopus citations

Abstract

At the 2011 Durham Conference "Geometry and Arithmetic of Lattices" M. Kapovich formulated the following Question. Does there exist an embedding ℤ² * ℤ Rightwards arrow with hook sign SL(3, ℤ)? The goal of the paper is to prove the following Main Theorem. If p and m are arbitrary positive integers then there exists an embedding ℤ² * F_m Rightwards arrow with hook sign SL(3, ℤ[1/p]).

Original language	English
Article number	1250057
Journal	International Journal of Algebra and Computation
Volume	22
Issue number	7
DOIs	https://doi.org/10.1142/S0218196712500579
State	Published - Nov 2012

Bibliographical note

Funding Information:
The author would like to thank several institutions and foundations for their support: SFB 701 “Spektrale Strukturen und Topologische Methoden in der Mathe-matik”, USA-Israel Binational Science foundation under BSF grant 2004010, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University and the Israel Science Foundation under ISF grant 657/09 and Max Planck Institute for Mathematics, Bonn. I would like to thank the referees for very helpful suggestions and comments.

Keywords

Arithmetic subgroups
free products
free subgroups
lattices

Access to Document

10.1142/S0218196712500579

Cite this

@article{4b0b2821d5ce479da058e13a96012f83,

title = "Embedding ℤ2 * Z as a discrete subgroup into small linear groups",

abstract = "At the 2011 Durham Conference {"}Geometry and Arithmetic of Lattices{"} M. Kapovich formulated the following Question. Does there exist an embedding ℤ2 * ℤ Rightwards arrow with hook sign SL(3, ℤ)? The goal of the paper is to prove the following Main Theorem. If p and m are arbitrary positive integers then there exists an embedding ℤ2 * Fm Rightwards arrow with hook sign SL(3, ℤ[1/p]).",

keywords = "Arithmetic subgroups, free products, free subgroups, lattices",

author = "Soifer, {G. A.}",

note = "Funding Information: The author would like to thank several institutions and foundations for their support: SFB 701 “Spektrale Strukturen und Topologische Methoden in der Mathe-matik”, USA-Israel Binational Science foundation under BSF grant 2004010, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University and the Israel Science Foundation under ISF grant 657/09 and Max Planck Institute for Mathematics, Bonn. I would like to thank the referees for very helpful suggestions and comments.",

year = "2012",

month = nov,

doi = "10.1142/S0218196712500579",

language = "אנגלית",

volume = "22",

journal = "International Journal of Algebra and Computation",

issn = "0218-1967",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "7",

}

TY - JOUR

T1 - Embedding ℤ2 * Z as a discrete subgroup into small linear groups

AU - Soifer, G. A.

N1 - Funding Information: The author would like to thank several institutions and foundations for their support: SFB 701 “Spektrale Strukturen und Topologische Methoden in der Mathe-matik”, USA-Israel Binational Science foundation under BSF grant 2004010, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University and the Israel Science Foundation under ISF grant 657/09 and Max Planck Institute for Mathematics, Bonn. I would like to thank the referees for very helpful suggestions and comments.

PY - 2012/11

Y1 - 2012/11

N2 - At the 2011 Durham Conference "Geometry and Arithmetic of Lattices" M. Kapovich formulated the following Question. Does there exist an embedding ℤ2 * ℤ Rightwards arrow with hook sign SL(3, ℤ)? The goal of the paper is to prove the following Main Theorem. If p and m are arbitrary positive integers then there exists an embedding ℤ2 * Fm Rightwards arrow with hook sign SL(3, ℤ[1/p]).

AB - At the 2011 Durham Conference "Geometry and Arithmetic of Lattices" M. Kapovich formulated the following Question. Does there exist an embedding ℤ2 * ℤ Rightwards arrow with hook sign SL(3, ℤ)? The goal of the paper is to prove the following Main Theorem. If p and m are arbitrary positive integers then there exists an embedding ℤ2 * Fm Rightwards arrow with hook sign SL(3, ℤ[1/p]).

KW - Arithmetic subgroups

KW - free products

KW - free subgroups

KW - lattices

UR - http://www.scopus.com/inward/record.url?scp=84870586688&partnerID=8YFLogxK

U2 - 10.1142/S0218196712500579

DO - 10.1142/S0218196712500579

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84870586688

SN - 0218-1967

VL - 22

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 7

M1 - 1250057

ER -