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We assign names and new generators to the transitive groups of degree up to 15, reflecting their structure.
We give a presentation of length O log 2 |G| for the groups G ∼ = PSU 3 (q). This result has applications in recent algorithms to compute the structure of permutation groups and matrix groups.
The lifting of results from factor groups to the full group is a standard technique for solvable groups. This paper shows how to utilize this approach in the case of non-solvable normal subgroups to compute the conju-gacy classes of a finite group.
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 introduce a new algorithm to compute up to conjugacy the maximal subgroups of a finite permutation group. Or method uses a " hybrid group " approach; that is, we first compute a large solvable normal subgroup of the given permutation group and then use this to split the computation in various parts.
We prove that the simple group L3(5) which has order 372000 is efficient by providing an efficient presentation for it. This leaves one simple group with order less than one million, S4(4) which has order 979200, whose efficiency or otherwise remains to be determined.