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Let E, F be Zp-fields of CM-type such that E/F is an extension of degree p. Let L, the normal closure of E/F, be such that Gal(L/F) has a normal subgroup of order p. Denote the fixed field of this group by K. We prove a Kida type formula which describes the minus part of the Iwasawa lambda invariant of E in terms of the lambda invariants of F and K.

Kida’s theorem for a class of nonnormal extensions