## 11R29 Class numbers, class groups, discriminants

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- On the Second Class Group of Real Quadratic Number Fields (2012)
- This thesis generalizes the Cohen-Lenstra heuristic for the class groups of real quadratic number fields to higher class groups. A "good part" of the second class group is defined. In general this is a non abelian proper factor group of the second class group. Properties of those groups are described, a probability distribution on the set of those groups is in- troduced and proposed as generalization of the Cohen-Lenstra heuristic for real quadratic number fields. The calculation of number field tables which contain information about higher class groups is explained and the tables are compared to the heuristic. The agree- ment is close. A program which can create an internet database for number field tables is presented.