Infinite Hilbert Class Field Towers over Cyclotomic Fields
نویسنده
چکیده
Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower over (exp(2π i/m)) for some p ≥ m0.3385+o(1). These results have immediate applications to the divisibility properties of the class number of (exp(2π i/m)). 2000 Mathematics Subject Classification. 11N25, 11R17, 11R37.
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