Generating fast Fourier transforms of solvable groups (Q597054)

The authors present a new algorithm for constructing a complete list of pairwise inequivalent ordinary irreducible representations of a finite solvable group \(G\). They give a rough analysis and worst-case complexity bounds. The output of the algorithm is well suited to performing a fast Fourier transform of \(G\). For supersolvable groups the disrete Fourier transform generation is much easier and can be done in a time which is --- up to logarithmic factors --- propontial to the output length. The authors also report on a recent implementation for the case of supersolvable groups.