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On some polycyclic groups with small Hirsch length

Heguo Liu

Department of Mathematics, Hubei University, Wuhan 430062, P. R. China

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Fang Zhou

Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, P. R. China

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, and

Tao Xu

Department of Science, Hebei University of Engineering, Handan 056038, P. R. China

E-mail Address: gtxutao@163.com

Corresponding author.

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https://doi.org/10.1142/S0219498817502371Cited by:0 (Source: Crossref)

Abstract

A polycyclic group $G$ is called an $N A F Q_{n}$ -group if every normal abelian subgroup of any finite quotient of $G$ is generated by $n$ , or fewer, elements and $n$ is the least integer with this property. In this paper, the structure of $N A F Q_{1}$ -groups and $N A F Q_{2}$ -groups is determined.

Communicated by D. S. Passman

Keywords:

AMSC: 20F19

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