Abstract
1. Introduction. Let p be a prime number and $ℤ_p$ the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, $k_{∞}$ a $ℤ_p$-extension of k, $k_n$ the nth layer of $k_{∞}/k$, and $A_n$ the p-Sylow subgroup of the ideal class
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