Abstract Let 𝑝 be an odd prime such that the Greenberg conjecture holds for the maximal real cyclotomic subfield 𝕂₁ of ℚ[𝜁𝑝]. Let 𝐴𝑛 = (𝐶(𝕂𝑛))𝑝 be the 𝑝-part of the class group of 𝕂𝑛, the ...