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ON THE p-CLASS GROUP STABILITY ALONG CYCLIC p-TOWERS OF A NUMBER FIELD
Let k be a number field and let p ≥ 2 be a prime number. We call K/k a (pro)-cyclic p-tower if Gal(K/k)~ Z/p^N Z or Z_p. We give an elementary proof of a stability theorem about generalized p-class groups in the tower (Main Theorem 3.1). This result, using generalizations …