This paper presents a new algorithm to classify all transitive subgroups of the symmetric group up to conjugacy. It has been used to determine the transitive groups of degree up to 30.
This article describes an algorithm for computing up to conjugacy all subgroups of a finite solvable group that are invariant under a set of automorphisms. It constructs the subgroups stepping down along a normal chain with elementary abelian factors.
This note presents a new algorithm for the computation of the set of normal subgroups of a finite group. It is based on lifting via homomorphic images.
We show how to compute efficiently a lexicographic ordering for subgroups and cosets of permutation groups and, more generally, of finite groups with a faithful permutation representation.
Constructive and nonconstructive techniques are employed to enumerate Latin squares and related objects. It is established that there are (i) 2036029552582883134196099 main classes of Latin squares of order 11; (ii) 6108088657705958932053657 isomorphism classes of one-factorizations of K 11,11 ; (iii) 12216177315369229261482540 isotopy classes of Latin… (More)
This paper describes an effective method for enumerating all composition series of a finite group, possibly up to action of a group of automorphisms. By building the series in an ascending way it only requires a very easy case of complement computation and can avoid the need to fuse subspace chains in vector spaces. As a by-product it also enumerates all… (More)
We construct generators for symplectic and orthogonal groups over residue class rings modulo an odd prime power. These generators have been implemented and are available in the computer algebra system GAP.