Reflections on Discriminating Groups

Gilbert Baumslag; Benjamin Fine; Anthony M. Gaglione; Dennis Spellman

doi:10.1515/JGT.2007.008

Reflections on Discriminating Groups

Gilbert Baumslag, Benjamin Fine, Anthony M. Gaglione, Dennis Spellman

Fairfield University

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

Abstract

Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in [7]. First we give examples of finitely generated groups which are discriminating but not trivially discriminating, in the sense that they do not embed their direct squares, and then we show how to generalize these examples. In the opposite direction we show that if F is a non-abelian free group and R is a normal subgroup of F such that F/R is torsion-free, then F/R' is non-discriminating.

Original language	American English
Journal	Journal of Group Theory
Volume	10
DOIs	https://doi.org/10.1515/JGT.2007.008
State	Published - Jan 1 2007

Disciplines

Computer Sciences
Physical Sciences and Mathematics

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10.1515/JGT.2007.008License: CC BY

Reflections on Discriminating GroupsFinal published version, 150 KBLicense: CC BY

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title = "Reflections on Discriminating Groups",

abstract = " Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in [7]. First we give examples of finitely generated groups which are discriminating but not trivially discriminating, in the sense that they do not embed their direct squares, and then we show how to generalize these examples. In the opposite direction we show that if F is a non-abelian free group and R is a normal subgroup of F such that F/R is torsion-free, then F/R' is non-discriminating.",

author = "Gilbert Baumslag and Benjamin Fine and Gaglione, \{Anthony M.\} and Dennis Spellman",

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AU - Fine, Benjamin

AU - Gaglione, Anthony M.

AU - Spellman, Dennis

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N2 - Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in [7]. First we give examples of finitely generated groups which are discriminating but not trivially discriminating, in the sense that they do not embed their direct squares, and then we show how to generalize these examples. In the opposite direction we show that if F is a non-abelian free group and R is a normal subgroup of F such that F/R is torsion-free, then F/R' is non-discriminating.

AB - Here we continue the study of discriminating groups as introduced by Baumslag, Myasnikov and Remeslennikov in [7]. First we give examples of finitely generated groups which are discriminating but not trivially discriminating, in the sense that they do not embed their direct squares, and then we show how to generalize these examples. In the opposite direction we show that if F is a non-abelian free group and R is a normal subgroup of F such that F/R is torsion-free, then F/R' is non-discriminating.

UR - https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/5

U2 - 10.1515/JGT.2007.008

DO - 10.1515/JGT.2007.008

M3 - Article

VL - 10

JO - Journal of Group Theory

JF - Journal of Group Theory

ER -

Reflections on Discriminating Groups

Abstract

Disciplines

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