Relative Galois module structure of rings of integers of absolutely abelian number fields

Let L/K be an extension of number fields where L/ℚ is abelian. We define such an extension to be Leopoldt if the ring of integers L of L is free over the associated order . Furthermore we define an abelian number field K to be Leopoldt if every finite extension L/K with L/ℚ abelian is Leopoldt in th...