Decidability for ℤ2G-lattices when G Extends the Noncyclic Group of Order 4

✍ Scribed by Annalisa Marcja; Carlo Toffalori

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 189 KB
• Volume: 48
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/1521-3870(200202)48:2<203::aid-malq203>3.0.co;2-v

✦ Synopsis

Let G be the direct sum of the noncyclic group of order four and a cyclic group whose order is the power p n of some prime p. We show that Z2 G-lattices have a decidable theory when the cyclotomic polynomial Φ j p (x) is irreducible modulo 2Z for every j ≤ n. More generally we discuss the decision problem for Z2 G-lattices when G is a finite group whose Sylow 2-subgroups are isomorphic to the noncyclic group of order four.