# Nonabelian Cohen–Lenstra moments

@article{Wood2019NonabelianCM,
title={Nonabelian Cohen–Lenstra moments},
author={Melanie Matchett Wood and Philip Matchett Wood},
journal={Duke Mathematical Journal},
year={2019}
}
• Published 15 February 2017
• Mathematics
• Duke Mathematical Journal
In this paper we give a conjecture for the average number of unramified $G$-extensions of a quadratic field for any finite group $G$. The Cohen-Lenstra heuristics are the specialization of our conjecture to the case that $G$ is abelian of odd order. We prove a theorem towards the function field analog of our conjecture, and give additional motivations for the conjecture including the construction of a lifting invariant for the unramified $G$-extensions that takes the same number of values as…

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### Moments of unramified 2-group extensions of quadratic fields

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