For abelian Galois groups Γ, the p-class group splits into a ramification-forced part with infinite average rank and a conjecturally Cohen-Lenstra distributed part; a weighted moment version is proved over F_q(t).
Wright, Distribution of discriminants of abelian extensions , Proc
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On the Distribution of Class Groups of Abelian Extensions
For abelian Galois groups Γ, the p-class group splits into a ramification-forced part with infinite average rank and a conjecturally Cohen-Lenstra distributed part; a weighted moment version is proved over F_q(t).