A defining property of virtually nilpotent groups

Beata Bajorska; Olga MacEdońska; Witold Tomaszewski

doi:10.5486/PMD.2012.5285

A defining property of virtually nilpotent groups

Beata Bajorska
, Olga MacEdońska
, Witold Tomaszewski

Department of Mathematics (RMS/RMS1)

Silesian University of Technology

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

2 Citations (Scopus)

Abstract

We answer the question: which property distinguishes the virtually nil- potent groups among the locally graded groups? The common property of each finitely generated group to have a finitely generated commutator subgroup is not sufficient. However, the finitely generated commutator subgroup of F ₂(varG), a free group of rank 2 in the variety defined by G, is the necessary and sufficient condition.

Original language	English
Pages (from-to)	415-420
Number of pages	6
Journal	Publicationes Mathematicae Debrecen
Volume	81
Issue number	3-4
DOIs	https://doi.org/10.5486/PMD.2012.5285
Publication status	Published - 2012

Keywords

Free groups in varieties
Locally graded groups
Virtually nilpotent groups

ASJC Scopus subject areas

General Mathematics

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10.5486/PMD.2012.5285

Cite this

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abstract = "We answer the question: which property distinguishes the virtually nil- potent groups among the locally graded groups? The common property of each finitely generated group to have a finitely generated commutator subgroup is not sufficient. However, the finitely generated commutator subgroup of F 2(varG), a free group of rank 2 in the variety defined by G, is the necessary and sufficient condition.",

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AU - Bajorska, Beata

AU - MacEdońska, Olga

AU - Tomaszewski, Witold

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N2 - We answer the question: which property distinguishes the virtually nil- potent groups among the locally graded groups? The common property of each finitely generated group to have a finitely generated commutator subgroup is not sufficient. However, the finitely generated commutator subgroup of F 2(varG), a free group of rank 2 in the variety defined by G, is the necessary and sufficient condition.

AB - We answer the question: which property distinguishes the virtually nil- potent groups among the locally graded groups? The common property of each finitely generated group to have a finitely generated commutator subgroup is not sufficient. However, the finitely generated commutator subgroup of F 2(varG), a free group of rank 2 in the variety defined by G, is the necessary and sufficient condition.

KW - Free groups in varieties

KW - Locally graded groups

KW - Virtually nilpotent groups

UR - https://www.scopus.com/pages/publications/84867551124

U2 - 10.5486/PMD.2012.5285

DO - 10.5486/PMD.2012.5285

M3 - Article

AN - SCOPUS:84867551124

SN - 0033-3883

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SP - 415

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JO - Publicationes Mathematicae Debrecen

JF - Publicationes Mathematicae Debrecen

IS - 3-4

ER -

A defining property of virtually nilpotent groups

Abstract

Keywords

ASJC Scopus subject areas

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