The Cohen-Lenstra Heuristic: Methodology and Results

الأصل · EN

In number theory, great efforts have been undertaken to study the Cohen-Lenstra probability measure on the set of all finite abelian p-groups. On the other hand, group theorists have studied a probability measure on the set of all partitions induced by the probability that a randomly chosen n× n-matrix over ₚ is contained in a conjucagy class associated with this partitions, for n → ∞. This paper shows that both probability measures are identical. As a consequence, a multitide of results can be transferred from each theory to the other one. The paper contains a survey about the known methods to study the probability measure and about the results that have been obtained so far, from both communities.