Elementary equivalence for finitely generated nilpotent groups and multilinear maps

Content Provider	Scilit
Author	Oger, Francis
Copyright Year	1998
Description	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 $(A_{1}$, …, $A_{n+1}$, f), where $A_{1}$, …, $A_{n+1}$ are disjoint finitely generated Abelian groups and f: $A_{1}$ × … × $A_{n}$ → $A_{n+1}$ is a n-linear map;(2) the triples (A, B, f), where A, B are disjoint finitely generated Abelian groups and f: $A^{n}$ → B is a n-linear map;(3) the pairs (A, f), where A is a finitely generated Abelian group and f: $A^{n}$ → A is a n-linear map.In the proof, we use some properties of commutative rings associated to multilinear maps.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/DF21EE1CF869ECC75322F8EC42822BA9/S0004972700032469a.pdf/div-class-title-elementary-equivalence-for-finitely-generated-nilpotent-groups-and-multilinear-maps-div.pdf
Ending Page	493
Page Count	15
Starting Page	479
ISSN	00049727
e-ISSN	17551633
DOI	10.1017/s0004972700032469
Journal	Bulletin of the Australian Mathematical Society
Issue Number	3
Volume Number	58
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1998-12-01
Access Restriction	Open
Subject Keyword	Bulletin of the Australian Mathematical Society Finitely Generated
Content Type	Text
Resource Type	Article
Subject	Mathematics