The global Cohen-Lenstra heuristic

JOURNAL OF ALGEBRA

卷:357

Article

Lengler, Johannes

关键词: Finite abelian group;    Cohen-Lenstra measure;    Probability measure;    Statistic behavior of class groups of number fields;   

DOI  :  10.1016/j.jalgebra.2012.01.036

来源: Elsevier

【 摘 要 】

The Cohen-Lenstra heuristic is a universal principle that assigns to each group a probability that tells how often this group should occur in nature. The most important, but not the only, applications are sequences of class groups, which conjecturally behave like random sequences of groups with respect to the so-called Cohen-Lenstra probability measure. So far, it was only possible to define this probability measure for finite abelian p-groups. We prove that it is also possible to define an analogous probability measure on the set of all finite abelian groups when restricting to the Sigma-algebra on the set of all finite abelian groups that is generated by uniform properties. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free