The Cohen–Lenstra heuristic: Methodology and results

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 Fp is contained in a conjugacy class associated with this partitions, for n→∞.This paper shows that both probability measures are identical. As a consequence, a multitude 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.