# [seqfan] Comment on A068982 and The Global Cohen-Lenstra Heuristic

Jonathan Post jvospost3 at gmail.com
Sat Jan 2 19:29:23 CET 2010

on p.14 Lengler derives A068982  Limit of the product of a modified

http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.4977v1.pdf

arXiv:0912.4977 [ps, pdf, other]
Title: The Global Cohen-Lenstra Heuristic
Authors: Johannes Lengler
Subjects: Number Theory (math.NT); Probability (math.PR)

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 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 \emph{all}
finite abelian groups when restricting to the $\Sigma$-algebra on the
set of all finite abelian groups that is generated by uniform
properties, thereby solving a problem that was open since 1984.