(i.e., we reach the trivial subgroup), then the sifted permutation was a member of the group at the top of the chain. References Knuth, Donald E. "Efficient representation of perm groups". Combinatorica 11 (1991), no. 1, 33–43. Seress, A., Permutation Group Algorithms, Cambridge U Press, 2002. Sims, Charles C. "Computational methods in the study of permutation groups", in Computational Problems in Abstract Algebra, pp. 169–183, Pergamon, Oxford, 1970. Computational group theory Permutation groups