On Meta Abelian Fields of a Certain Type

Yoshiomi Furuta
1959 Nagoya mathematical journal  
Let k be an algebraic number field of finite degree, and l a rational prime (including 2); k and l being fixed throughout this paper. For any power ln of l, denote by ζn an arbitrarily fixed primitive ln-th root of unity, and put kn = k(ζn). Let r be the maximal rational integer such that ζr∈k i.e. kr = k and kr+1≠k.
doi:10.1017/s0027763000005845 fatcat:6rpc7wklwrftnhi4pyhqw72l5q