What is… the distribution of p-tower groups?
Vortrag von Luca Rubio
Datum: 13.05.25 Zeit: 16.30 - 18.30 Raum:
The p-tower group of an imaginary quadratic number field K is the Galois group over K of the maximal unramified pro-p extension of K. It is known that the abelianization of the p-tower group is naturally isomorphic to the p-primary part of the narrow ideal class group Cl_K[p]. The Cohen-Lenstra heuristics give a probabilistic explanation for how often Cl_K[p] is isomorphic to a given finite abelian p-group. The goal of this talk is to generalise the Cohen-Lenstra heuristics to the non-abelian case.