Simple groups in computational group theory (Q1126707)

This paper surveys many recent results which use structural properties of finite groups to create efficient algorithms for group theoretic computations. The author discusses applications of the classification of finite simple groups to computational group theory, emphasizing results where it is far from obvious how simple groups are relevant, and focusing on the mathematics behind the algorithms. Several theorems are stated with some discussion of the ideas involved in their proofs as well as connections between the results. Many of the theorems stated have the form ``There exists an algorithm \dots'' (followed by some type of efficiency statement about the algorithm as well as what it computes), but the author also discusses related nonalgorithmic theorems.