Schreier–Sims algorithm

Summary

The Schreier–Sims algorithm takes a few permutations that generate a permutation group $G$ and computes a base and a strong generating set of $G$. With this data one can find the order of $G$ and test whether a permutation belongs to $G$. This takes time polynomial in the degree and the number of generators. It is the basic algorithm of computational group theory, used in systems such as GAP and Magma. It is named after Otto Schreier and Charles Sims.