A compact representation for permutation groups
Journal of Algorithms
Finding composition factors of permutation groups of degree n≤106
Journal of Symbolic Computation - Special issue on computational group theory: part 2
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
The one-round functions of the DES generate the alternating group
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
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The availability of the classification of finite simple groups allows us to design algorithms for identifying the composition factors of finite groups. This paper presents an algorithm which identifies any finite doubly transitive permutation group G. If we exclude the 2-transitive subgroups of the one-dimensional affine group and 14 small exceptional groups, the cost of our algorithm is essentially the cost of constructing a base and strong generating set for G. Consequently, our algorithm avoids the need to compute the soluble residual of G as required by Kantor's composition factors algorithm for a general permutation group.