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Quasi-finitely axiomatizable nilpotent groups
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F Oger
and
G Sabbagh
Published/Copyright:
May 12, 2006
Abstract
In [], A. Nies introduces the notion of a quasi-finitely axiomatizable (QFA) group. He proves that the free nilpotent group of class 2 with 2 generators is QFA, and that it is a prime model of its theory. Our results, stated below in full generality, provide, in particular, a complete characterization of QFA nilpotent groups (in particular, any finitely generated nonabelian free nilpotent group is QFA). They imply that each finitely generated nilpotent group is QFA if and only if it is a prime model of its theory.
Received: 2004-07-08
Revised: 2005-01-27
Published Online: 2006-05-12
Published in Print: 2006-01-26
© Walter de Gruyter
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Articles in the same Issue
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Reduction theorems for Clifford classes
- Finite groups with NE-subgroups
- Jordan groups and limits of betweenness relations
- Quasi-finitely axiomatizable nilpotent groups
- Quasi-finitely axiomatizable groups and groups which are prime models
- The structure of Bell groups
- Groups with bounded verbal conjugacy classes
Articles in the same Issue
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Reduction theorems for Clifford classes
- Finite groups with NE-subgroups
- Jordan groups and limits of betweenness relations
- Quasi-finitely axiomatizable nilpotent groups
- Quasi-finitely axiomatizable groups and groups which are prime models
- The structure of Bell groups
- Groups with bounded verbal conjugacy classes
