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RESEARCH ARTICLE

On verbal subgroups of finitely generated nilpotent groups

Agnieszka Bier

Institute of Mathematics, Faculty of Mathematics and Physics, Silesian University of Technology, Poland

Abstract: The paper concerns the problem of characterization of verbal subgroups in finitely generated nilpotent groups. We introduce the notion of verbal poverty and show that every verbally poor finitely generated nilpotent group is a finite $p$-group with the lower $p$-central series for certain prime $p$. We conclude with few examples of verbally poor groups.

Keywords: finitely generated nilpotent groups, verbal subgroups.

MSC: 20D15, 20F18

Received: 15.05.2009
Revised: 08.10.2009

Language: English

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