# Lagrange and the Supernaturals

Friday, August 03rd, 2012 | Author: Konrad Voelkel

You might know the theorem of Lagrange from group theory: A finite group of order n can have a subgroup of order m only if m divides n. Here the order is just the number of elements, a natural number.

Recently I came across a generalization to profinite groups. How do you make sense of the order of an infinite group? How to say that the order of a subgroup divides the order of the group? The solution is a simple concept called supernatural numbers, which I will explain in this short article. The main part should in principle be accessible to non-mathematicians as well.

Category: English, Mathematics | 4 Comments