All Questions

Question. How many (isomorphism types of) finite groups of size at most n are there? What is the asymptotic growth rate? And the same question for rings, fields, graphs, partial orders, etc. ...

Let $ F_q $ be a finite field of characteristic 2. Let $ x^2 + Sx +P \in F_q[x] $ be an irreducible polynomial over $ F_q $, and let $ g $ be one of its roots in $ F_{q^2} $. Define a map $ M: F_{q^2}...