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Elementary Equivalence and Profinite Completions: A Characterization of Finitely Generated Abelian-by-Finite Groups
| Content Provider | Scilit |
|---|---|
| Author | Oger, Francis |
| Copyright Year | 1988 |
| Description | 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 which satisfy these properties while and 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. |
| Related Links | http://www.ams.org/proc/1988-103-04/S0002-9939-1988-0954980-0/S0002-9939-1988-0954980-0.pdf |
| Ending Page | 1048 |
| Page Count | 8 |
| Starting Page | 1041 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2047082 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 4 |
| Volume Number | 103 |
| Language | English |
| Publisher | Duke University Press |
| Access Restriction | Open |
| Subject Keyword | Logic Finite Groups Finitely Generated Abelian Elementary Equivalence Profinite Completions Equivalence and Profinite |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
