We shall consider the maximal cyclotomic extension of a totally real finite algebraic number field and its ideal class group. We shall investigate the structure of the ideal class group with the action of the cyclotomic Galois group.
Mamoru ASADA. "On the ideal class groups of the maximal cyclotomic extensions of algebraic number fields." J. Math. Soc. Japan 66 (4) 1091 - 1103, October, 2014. https://doi.org/10.2969/jmsj/06641091