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On existentially closed and generic nilpotent groups

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Abstract

Letn≧2 be an integer. We prove the following results that are known in casen=2: The upper and the lower central series of an existentially closed nilpotent group of classn coincide. A finitely generic nilpotent group of classn is periodic and the center of a finitely generic torsion-free nilpotent group of classn is isomorphic toQ +, whereas infinitely generic nilpotent groups do not enjoy these properties. We determine the structure of the torsion subgroup of existentially closed nilpotent groups of class 2. Finally we give an algebraic proof that there exist 2κ non-isomorphic existentially closed nilpotent groups of classn in cardinalityK ≧N 0.

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Authors and Affiliations

  1. Mathematisches Institut, Albertstrasse 23b, D-7800, Freiburg, FRG

    Berthold J. Maier

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  1. Berthold J. Maier
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Some results of this paper were contained in [6].

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Maier, B.J. On existentially closed and generic nilpotent groups. Israel J. Math. 46, 170–188 (1983). https://doi.org/10.1007/BF02761950

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  • DOI: https://doi.org/10.1007/BF02761950

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