Statistics of bad parts of class groups

TL;DR

This paper provides a formula for the 'bad part' of p-class groups applicable to all abelian p-extensions ordered by ramified primes, enhancing understanding of class group structures.

Contribution

It introduces a universal formula for the bad part of p-class groups in abelian p-extensions, valid for all cases when ordered by ramified primes.

Findings

Formula valid for 100% of abelian p-extensions

Applicable when ordered by product of ramified primes

Advances understanding of class group decomposition

Abstract

Let $p$ be an odd prime. We give a formula for the bad part of $p$-class groups that is valid for $100\%$ of the abelian $p$-extensions when ordered by product of ramified primes.