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

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10.1007/BF01058685

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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",

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doi = "10.1007/BF01058685",

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journal = "Ukrainian Mathematical Journal",

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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.

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Equations in a group with a length function

Abstract

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