Equations in a group with a length function

A. N. Zubkov; V. N. Remeslennikov

doi:10.1007/BF01058685

Equations in a group with a length function

A. N. Zubkov
, V. N. Remeslennikov

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

Abstract

A simple counterexample to Lyndon's conjecture is given. There is defined a group of continuous functions with a regular Archimedean length function. Analogues of Wicks' theorem on the commutator and of Lyndon's theorem on the solutions of the equation a²b²=c² are proved for a wider class of groups with a regular Archimedean length function.

Original language	English
Pages (from-to)	872-878
Number of pages	7
Journal	Ukrainian Mathematical Journal
Volume	43
Issue number	7-8
DOIs	https://doi.org/10.1007/BF01058685
Publication status	Published - Jul 1991
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/BF01058685

Cite this

@article{20440c38817945cfba424b4b0fb5583e,

title = "Equations in a group with a length function",

abstract = "A simple counterexample to Lyndon's conjecture is given. There is defined a group of continuous functions with a regular Archimedean length function. Analogues of Wicks' theorem on the commutator and of Lyndon's theorem on the solutions of the equation a2b2=c2 are proved for a wider class of groups with a regular Archimedean length function.",

author = "Zubkov, \{A. N.\} and Remeslennikov, \{V. N.\}",

year = "1991",

month = jul,

doi = "10.1007/BF01058685",

language = "English",

volume = "43",

pages = "872--878",

journal = "Ukrainian Mathematical Journal",

issn = "0041-5995",

publisher = "Springer New York",

number = "7-8",

}

TY - JOUR

T1 - Equations in a group with a length function

AU - Zubkov, A. N.

AU - Remeslennikov, V. N.

PY - 1991/7

Y1 - 1991/7

N2 - A simple counterexample to Lyndon's conjecture is given. There is defined a group of continuous functions with a regular Archimedean length function. Analogues of Wicks' theorem on the commutator and of Lyndon's theorem on the solutions of the equation a2b2=c2 are proved for a wider class of groups with a regular Archimedean length function.

AB - A simple counterexample to Lyndon's conjecture is given. There is defined a group of continuous functions with a regular Archimedean length function. Analogues of Wicks' theorem on the commutator and of Lyndon's theorem on the solutions of the equation a2b2=c2 are proved for a wider class of groups with a regular Archimedean length function.

UR - https://www.scopus.com/pages/publications/34249925138

UR - https://www.scopus.com/pages/publications/34249925138#tab=citedBy

U2 - 10.1007/BF01058685

DO - 10.1007/BF01058685

M3 - Article

AN - SCOPUS:34249925138

SN - 0041-5995

VL - 43

SP - 872

EP - 878

JO - Ukrainian Mathematical Journal

JF - Ukrainian Mathematical Journal

IS - 7-8

ER -

Equations in a group with a length function

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this