We shall consider the maximal cyclotomic extension of a finite algebraic number field and its two abelian extensions, the maximal abelian extension and the maximal abelian extension with certain restricted ramification. We shall investigate the structure of these Galois groups with the action of the cyclotomic Galois group.
"On Galois groups of abelian extensions over maximal cyclotomic fields." Tohoku Math. J. (2) 60 (1) 135 - 147, 2008. https://doi.org/10.2748/tmj/1206734410