Unit Groups of Cyclic Extensions

Tomio Kubota
1957 Nagoya mathematical journal  
LetΩbe an algebraic number field of finite degree, which we fix once for all, and letKbe a cyclic extension overΩsuch that the degree ofK/Ωis a powerof a prime numberl. It is obvious that the norm groupNK/ΩeKof the unit group ekofK, being a subgroup of the unit group e of Ω contains the groupconsisting of all-th powersof ε∈e.
doi:10.1017/s0027763000022078 fatcat:bqpruuqk35g6rncs5aaz222wam