An application of Iwasawa theory to constructing fields {${\bf Q}(\zeta\sb n+\zeta\sb n\sp {-1})$} which have class group with large {$p$}-rank

Abstract

Let $p$ be an odd prime number. By using Iwasawa theory, we shall construct cyclotomic fields whose maximal real subfields have class group with arbitrarily large $p$-rank and conductor with only four prime factors.