Discriminating Groups

Benjamin Fine; A. G. Myasnikov; Anthony M. Gaglione; Dennis Spellman

doi:10.1515/jgth.2001.034

Discriminating Groups

Benjamin Fine, A. G. Myasnikov, Anthony M. Gaglione, Dennis Spellman

Fairfield University

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

Abstract

A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups.

Original language	American English
Journal	Journal of Group Theory
Volume	4
DOIs	https://doi.org/10.1515/jgth.2001.034
State	Published - Jan 1 2001

Disciplines

Computer Sciences
Physical Sciences and Mathematics

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10.1515/jgth.2001.034License: CC BY

Discriminating GroupsFinal published version, 132 KBLicense: CC BY

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title = "Discriminating Groups",

abstract = " A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups.",

author = "Benjamin Fine and Myasnikov, \{A. G.\} and Gaglione, \{Anthony M.\} and Dennis Spellman",

year = "2001",

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doi = "10.1515/jgth.2001.034",

language = "American English",

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AU - Gaglione, Anthony M.

AU - Spellman, Dennis

PY - 2001/1/1

Y1 - 2001/1/1

N2 - A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups.

AB - A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups.

UR - https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/8

U2 - 10.1515/jgth.2001.034

DO - 10.1515/jgth.2001.034

M3 - Article

VL - 4

JO - Journal of Group Theory

JF - Journal of Group Theory

ER -

Discriminating Groups

Abstract

Disciplines

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