Some orbits of free words that are determined by measures on finite groups

Liam Hanany; Chen Meiri; Doron Puder

doi:10.1016/j.jalgebra.2020.03.013

Some orbits of free words that are determined by measures on finite groups

Liam Hanany, Chen Meiri, Doron Puder

Tel Aviv University, Technion - Israel Institute of Technology

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

Abstract

Every word in a free group F induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on every finite group, necessarily belong to the same orbit of AutF. A special case of this problem, when one of the words is the primitive word x, was settled positively by the third author and Parzanchevski [15]. Here we extend this result to the case where one of the words is x^d or [x,y]^d for an arbitrary d∈Z.

Original language	English
Pages (from-to)	305-324
Number of pages	20
Journal	Journal of Algebra
Volume	555
DOIs	https://doi.org/10.1016/j.jalgebra.2020.03.013
State	Published - 1 Aug 2020

Keywords

Free groups
Profinite groups

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2020.03.013

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title = "Some orbits of free words that are determined by measures on finite groups",

abstract = "Every word in a free group F induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on every finite group, necessarily belong to the same orbit of AutF. A special case of this problem, when one of the words is the primitive word x, was settled positively by the third author and Parzanchevski [15]. Here we extend this result to the case where one of the words is xd or [x,y]d for an arbitrary d∈Z.",

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AU - Meiri, Chen

AU - Puder, Doron

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N2 - Every word in a free group F induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on every finite group, necessarily belong to the same orbit of AutF. A special case of this problem, when one of the words is the primitive word x, was settled positively by the third author and Parzanchevski [15]. Here we extend this result to the case where one of the words is xd or [x,y]d for an arbitrary d∈Z.

AB - Every word in a free group F induces a probability measure on every finite group in a natural manner. It is an open problem whether two words that induce the same measure on every finite group, necessarily belong to the same orbit of AutF. A special case of this problem, when one of the words is the primitive word x, was settled positively by the third author and Parzanchevski [15]. Here we extend this result to the case where one of the words is xd or [x,y]d for an arbitrary d∈Z.

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KW - Profinite groups

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DO - 10.1016/j.jalgebra.2020.03.013

M3 - مقالة

SN - 0021-8693

VL - 555

SP - 305

EP - 324

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Some orbits of free words that are determined by measures on finite groups

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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