On Rationality of Verbal Subsets in a Group

A. Myasnikov; V. Roman'kov

doi:10.1007/s00224-012-9394-3

On Rationality of Verbal Subsets in a Group

A. Myasnikov, V. Roman'kov

Department of Mathematical Sciences

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

12 Scopus citations

Abstract

Let F be a free non-abelian group. We show that for any group word w the set w[F] of all values of w in F is rational in F if and only if w[F]=1 or w[F]=F. We generalize this to a wide class of free products of groups.

Original language	English
Pages (from-to)	587-598
Number of pages	12
Journal	Mathematical Systems Theory
Volume	52
Issue number	4
DOIs	https://doi.org/10.1007/s00224-012-9394-3
State	Published - May 2013

Keywords

Finite automata
Free groups
Free products
Verbal sets

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10.1007/s00224-012-9394-3

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abstract = "Let F be a free non-abelian group. We show that for any group word w the set w[F] of all values of w in F is rational in F if and only if w[F]=1 or w[F]=F. We generalize this to a wide class of free products of groups.",

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AU - Myasnikov, A.

AU - Roman'kov, V.

PY - 2013/5

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N2 - Let F be a free non-abelian group. We show that for any group word w the set w[F] of all values of w in F is rational in F if and only if w[F]=1 or w[F]=F. We generalize this to a wide class of free products of groups.

AB - Let F be a free non-abelian group. We show that for any group word w the set w[F] of all values of w in F is rational in F if and only if w[F]=1 or w[F]=F. We generalize this to a wide class of free products of groups.

KW - Finite automata

KW - Free groups

KW - Free products

KW - Verbal sets

UR - https://www.scopus.com/pages/publications/84876130837

UR - https://www.scopus.com/inward/citedby.url?scp=84876130837&partnerID=8YFLogxK

U2 - 10.1007/s00224-012-9394-3

DO - 10.1007/s00224-012-9394-3

M3 - Article

AN - SCOPUS:84876130837

SN - 1432-4350

VL - 52

SP - 587

EP - 598

JO - Mathematical Systems Theory

JF - Mathematical Systems Theory

IS - 4

ER -

On Rationality of Verbal Subsets in a Group

Abstract

Keywords

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