F][[GAMMA]]), and it implies that when p [greater than or equal to] 5, an imaginary abelian field F satisfies ([H.
M] the relative class number when M is an imaginary abelian field.
At present, we have no example of an abelian field F which satisfies ([H.
Sinnott, On the Stickelberger ideal and the circular units of an abelian field, Invent.
The main purpose of this note is to deal with real abelian fields satisfying ([H.
1] mentioned above, we obtain the following assertion using some computational results on abelian fields.