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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Wreath products and existentially complete solvable groups


Author: D. Saracino
Journal: Trans. Amer. Math. Soc. 197 (1974), 327-339
MSC: Primary 02H15; Secondary 20E15
DOI: https://doi.org/10.1090/S0002-9947-1974-0342391-5
MathSciNet review: 0342391
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Abstract: It is known that the theory of abelian groups has a model companion but that the theory of groups does not. We show that for any fixed $ n \geq 2$ the theory of groups solvable of length $ \leq n$ has no model companion. For the metabelian case $ (n = 2)$ we prove the stronger result that the classes of finitely generic, infinitely generic, and existentially complete metabelian groups are all distinct. We also give some algebraic results on existentially complete metabelian groups.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0342391-5
Keywords: Model companion, wreath product, ultraproduct, finite forcing, infinite forcing, existential completeness
Article copyright: © Copyright 1974 American Mathematical Society

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