### Sublattices and subrings of Z^n and random finite abelian groups (Nathan Kaplan, UC Irvine)

Estella 2099How many sublattices of Zn have index at most X? If we choose such a lattice L at random, what is the probability that Zn/L is cyclic? What is the probability that its order is odd? Now let R be a random subring of Zn. What is the probability that Zn/R is cyclic? We will see how these questions fit […]