Probabilistically nilpotent groups

Aner Shalev

doi:10.1090/proc/13867

Probabilistically nilpotent groups

Aner Shalev

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We show that, for a finitely generated residually finite group Γ, the word [x1,…, xk] is a probabilistic identity of Γ if and only if Γ has a finite index subgroup which is nilpotent of class less than k. Related results, generalizations and problems are also discussed.

Original language	English
Pages (from-to)	1529-1536
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	4
DOIs	https://doi.org/10.1090/proc/13867
State	Published - 2018

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Access to Document

10.1090/proc/13867

Cite this

@article{5b18d71828074ec49c0917debbaec22c,

title = "Probabilistically nilpotent groups",

abstract = "We show that, for a finitely generated residually finite group Γ, the word [x1,…, xk] is a probabilistic identity of Γ if and only if Γ has a finite index subgroup which is nilpotent of class less than k. Related results, generalizations and problems are also discussed.",

author = "Aner Shalev",

note = "Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2018",

doi = "10.1090/proc/13867",

language = "الإنجليزيّة",

volume = "146",

pages = "1529--1536",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "4",

}

TY - JOUR

T1 - Probabilistically nilpotent groups

AU - Shalev, Aner

PY - 2018

Y1 - 2018

N2 - We show that, for a finitely generated residually finite group Γ, the word [x1,…, xk] is a probabilistic identity of Γ if and only if Γ has a finite index subgroup which is nilpotent of class less than k. Related results, generalizations and problems are also discussed.

AB - We show that, for a finitely generated residually finite group Γ, the word [x1,…, xk] is a probabilistic identity of Γ if and only if Γ has a finite index subgroup which is nilpotent of class less than k. Related results, generalizations and problems are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=85041518717&partnerID=8YFLogxK

U2 - 10.1090/proc/13867

DO - 10.1090/proc/13867

M3 - مقالة

SN - 0002-9939

VL - 146

SP - 1529

EP - 1536

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Probabilistically nilpotent groups

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this