Abelian‐by‐ G  Groups, for  G  Finite, from the Model Theoretic Point of View | Zendy

Marcja Annalisa | Zendy; Toffalori Carlo | Zendy

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Abelian‐by‐ G Groups, for G Finite, from the Model Theoretic Point of View

Author(s) -

Marcja Annalisa,

Toffalori Carlo

Publication year - 1994

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19940400117

Subject(s) - abelian group , mathematics , decidability , elementary abelian group , square free integer , mathematics subject classification , class (philosophy) , group (periodic table) , combinatorics , order (exchange) , discrete mathematics , pure mathematics , physics , computer science , finance , quantum mechanics , artificial intelligence , economics

Let G be a finite group. We prove that the theory af abelian‐by‐ G groups is decidable if and only if the theory of modules over the group ring ℤ[ G ] is decidable. Then we study some model theoretic questions about abelian‐by‐ G groups, in particular we show that their class is elementary when the order of G is squarefree. Mathematics Subject Classification: 03C60, 03B25.

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