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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.