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Elementary equivalence for finitely generated nilpotent groups and multilinear maps
- Source :
- Bulletin of the Australian Mathematical Society. 58:479-493
- Publication Year :
- 1998
- Publisher :
- Cambridge University Press (CUP), 1998.
-
Abstract
- We show that two finitely generated finite-by-nilpotent groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. For each integer n ≥ 2, we prove the same result for the following classes of structures:(1) the (n + 2)-tuples (A1, …, An+1, f), where A1, …, An+1 are disjoint finitely generated Abelian groups and f: A1 × … × An → An+1 is a n-linear map;(2) the triples (A, B, f), where A, B are disjoint finitely generated Abelian groups and f: An → B is a n-linear map;(3) the pairs (A, f), where A is a finitely generated Abelian group and f: An → A is a n-linear map.In the proof, we use some properties of commutative rings associated to multilinear maps.
Details
- ISSN :
- 17551633 and 00049727
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- Bulletin of the Australian Mathematical Society
- Accession number :
- edsair.doi...........347c262b7452a6fc401f8f00e465429f
- Full Text :
- https://doi.org/10.1017/s0004972700032469