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- W4252840410 abstract "In this paper, we show that any finitely generated abelian-by-finite group is an elementary submodel of its profinite completion. It follows that two finitely generated abelian-by-finite groups are elementarily equivalent if and only if they have the same finite images. We give an example of two finitely generated abelian-by-finite groups $G,H$ which satisfy these properties while $G times {bf {Z}}$ and $G times {bf {Z}}$ are not isomorphic. We also prove that a finitely generated nilpotent-by-finite group is elementarily equivalent to its profinite completion if and only if it is abelian-by-finite." @default.
- W4252840410 created "2022-05-12" @default.
- W4252840410 creator A5084063599 @default.
- W4252840410 date "1988-08-01" @default.
- W4252840410 modified "2023-10-17" @default.
- W4252840410 title "Elementary Equivalence and Profinite Completions: A Characterization of Finitely Generated Abelian-by-Finite Groups" @default.
- W4252840410 doi "https://doi.org/10.2307/2047082" @default.
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