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Decidability for ℤ 2 G ‐lattices when G Extends the Noncyclic Group of Order 4
Author(s) -
Marcja Annalisa,
Toffalori Carlo
Publication year - 2002
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 - 10.1002/1521-3870(200202)48:2<203::aid-malq203>3.0.co;2-v
Subject(s) - mathematics , sylow theorems , decidability , modulo , order (exchange) , combinatorics , prime (order theory) , group (periodic table) , cyclic group , discrete mathematics , finite group , abelian group , chemistry , organic chemistry , finance , economics
Let G be the direct sum of the noncyclic groupof order four and a cyclic groupwhoseorderisthe power p n of some prime p . We show that ℤ 2 G ‐lattices have a decidable theory when the cyclotomic polynomia $ \Phi ^{j} _{p} $ ( x ) is irreducible modulo 2ℤ for every j ≤ n . More generally we discuss the decision problem for ℤ 2 G ‐lattices when G is a finite group whose Sylow 2‐subgroups are isomorphic to the noncyclic group of order four.