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Some remarks on the computation of conjugacy classes of soluble groups

Laue et al have described basic algorithms for computing in a finite soluble group G given by an AG-presentation, among them a general algorithm for the computation of the orbits of such a group acting on some set Ω. Among other applications, this algorithm yields straightforwardly a method for the computation of the conjugacy classes of elements in such a group, which has been implemented in 1986 in FORTRAN within SOGOS by the first author and in 1987 in C within CAYLEY. However, for this particular problem one can do better, as discussed in this note.