Elementary equivalence for finitely generated nilpotent groups and multilinear maps
1998 ◽
Vol 58
(3)
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pp. 479-493
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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.
2011 ◽
Vol 10
(03)
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pp. 377-389
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1996 ◽
Vol 19
(3)
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pp. 539-544
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2013 ◽
Vol 56
(3)
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pp. 477-490
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1969 ◽
Vol 21
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pp. 712-729
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2002 ◽
Vol 72
(2)
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pp. 173-180
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1975 ◽
Vol 78
(3)
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pp. 357-368
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