Computation of the -part of the ideal class group of certain real abelian fields

Under Greenberg's conjecture, we give an efficient method to compute the -part of the ideal class group of certain real abelian fields by using cyclotomic units, Gauss sums and prime numbers. As numerical examples, we compute the -part of the ideal class group of the maximal real subfield of in the range and . In order to explain our method, we show an example whose ideal class group is not cyclic.