K-Admissibility of Wreath Products of Cyclicp-Groups Original Research Article

LetKbe a number field and letGbe a wreath product of cyclicp-groups. We show that ifpis odd, thenGisK-admissible if and only ifGis cyclic orphas at least two divisors inK. Ifp=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 forp=2, that a metacyclicp-groupGisK-admissible if and only if it occurs as a Galois group over two completions ofK. In addition, we prove that the property ofK-admissibility is inherited by metacyclicp-subgroups.