Abstract
We consider the Galois group of the maximal unramified 2-extension of K where is cyclic of degree 3. We also consider the group where ramification is allowed at infinity. In the spirit of the Cohen–Lenstra heuristics, we identify certain types of groups as the natural spaces where and live when the 2-class group of K is 2-generated. While we do not have a theoretical scheme for assigning probabilities, we present data and make some observations and conjectures about the distribution of such groups.
Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.
Acknowledgments
We thank Brandon Alberts, Jordan Ellenberg, Farshid Hajir, Yuan Liu, John Voight, Jiuya Wang, and Melanie Matchett Wood for helpful conversations and feedback. We also thank the anonymous referees for their careful reading of the article and for making a number of helpful suggestions that improved the exposition. The work of MRB was partially supported by summer Lenfest Grants from Washington and Lee University.
Declaration of Interest
No potential conflict of interest was reported by the author(s).