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Elementary equivalence for finitely generated nilpotent groups and multilinear maps

Authors :
Francis Oger
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