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In this paper, we study the Iwasawa Formula: see text-invariant of the cyclotomic Formula: see text-extension of Formula: see text, where Formula: see text are distinct odd prime numbers satisfying certain arithmetic conditions. Moreover, we obtain an upper bound of the Formula: see text-part of the class number of certain quartic number fields by calculating the Sinnott index explicitly.
Naoki Kumakawa (Wed,) studied this question.