K-Admissibility of Wreath Products of Cyclicp-Groups

✍ Scribed by Steven Liedahl

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 801 KB
• Volume: 60
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1996.0120

✦ Synopsis

Let K be a number field and let G be a wreath product of cyclic p-groups. We show that if p is odd, then G is K-admissible if and only if G is cyclic or p has at least two divisors in K. If p=2 we obtain a similar partial result. This work relies on a determination of the Galois structure of the group of l-units in certain local fields. The main theorem is used to prove our conjecture, which was open for p=2, that a metacyclic p-group G is K-admissible if and only if it occurs as a Galois group over two completions of K. In addition, we prove that the property of K-admissibility is inherited by metacyclic p-subgroups.