Computing chief series, composition series and socles in large permutation groups (Q1369791)

This paper describes the theory and implementation of algorithms for computing chief series, composition series, and socles in large permutation groups. The authors are more concerned with the practical efficiency of the algorithm in actual computation than with the worst-case complexity (and they assume that the degree of the permutation group is not more than \(10^7\)), but they give references where most parts of the algorithm have been proven to be polynomial time. Most of their algorithms have been implemented in the Magma Computational Algebra System and the paper includes some tables of running time on various examples, showing that the algorithms can be practical on groups whose degree is in the hundreds of thousands. Several of the ideas involved are based on an algorithm of \textit{W. M. Kantor} [J. Symb. Comput. 12, No. 4/5, 517-526 (1991; Zbl 0792.20003)].