On asymptotic properties of verbal subsets in a group

A. Myasnikov; V. Roman’kov

doi:10.1134/S1995080215040113

On asymptotic properties of verbal subsets in a group

A. Myasnikov
, V. Roman’kov

Department of Mathematical Sciences

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

Abstract

We prove that the asymptotic density ρ(w[F_r]) of the verbal set w[F_r] in a free group F_r, r ≥ 2, is equal to 0 for every word w with exponent sum exp(w) ≠ 1. When exp(w) = 1 one has w[F_r] = F_r, and so ρ(w[F_r]) = 1.

Original language	English
Pages (from-to)	399-402
Number of pages	4
Journal	Lobachevskii Journal of Mathematics
Volume	36
Issue number	4
DOIs	https://doi.org/10.1134/S1995080215040113
State	Published - 1 Oct 2015

Keywords

asymptotic density
free group
verbal set

Access to Document

10.1134/S1995080215040113

Cite this

@article{7d5a7346fddc41e0a646a2a36c481da2,

title = "On asymptotic properties of verbal subsets in a group",

abstract = "We prove that the asymptotic density ρ(w[Fr]) of the verbal set w[Fr] in a free group Fr, r ≥ 2, is equal to 0 for every word w with exponent sum exp(w) ≠ 1. When exp(w) = 1 one has w[Fr] = Fr, and so ρ(w[Fr]) = 1.",

keywords = "asymptotic density, free group, verbal set",

author = "A. Myasnikov and V. Roman{\textquoteright}kov",

note = "Publisher Copyright: {\textcopyright} 2015, Pleiades Publishing, Ltd.",

year = "2015",

month = oct,

day = "1",

doi = "10.1134/S1995080215040113",

language = "English",

volume = "36",

pages = "399--402",

number = "4",

}

TY - JOUR

T1 - On asymptotic properties of verbal subsets in a group

AU - Myasnikov, A.

AU - Roman’kov, V.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - We prove that the asymptotic density ρ(w[Fr]) of the verbal set w[Fr] in a free group Fr, r ≥ 2, is equal to 0 for every word w with exponent sum exp(w) ≠ 1. When exp(w) = 1 one has w[Fr] = Fr, and so ρ(w[Fr]) = 1.

AB - We prove that the asymptotic density ρ(w[Fr]) of the verbal set w[Fr] in a free group Fr, r ≥ 2, is equal to 0 for every word w with exponent sum exp(w) ≠ 1. When exp(w) = 1 one has w[Fr] = Fr, and so ρ(w[Fr]) = 1.

KW - asymptotic density

KW - free group

KW - verbal set

UR - https://www.scopus.com/pages/publications/84949186815

UR - https://www.scopus.com/pages/publications/84949186815#tab=citedBy

U2 - 10.1134/S1995080215040113

DO - 10.1134/S1995080215040113

M3 - Article

AN - SCOPUS:84949186815

SN - 1995-0802

VL - 36

SP - 399

EP - 402

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

IS - 4

ER -

On asymptotic properties of verbal subsets in a group

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this