How many groups of order n are there, up to isomorphism? And what about quasigroups, semigroups, and other types of algebraic structures? Why the combinatorial explosion for quasigroups and semigroups, and not for groups? Or, actually, what is the true asymptotic behavior behind enumeration of groups? I will show some number series. I will briefly discuss enumeration methods. I will start with a brief overview of classical results on groups. In the second half of the talk, I will turn to the class of quandles, which provides an exciting playground for various types of enumeration methods.
Enumeration of groups and quandles