Computing a set of generators of minimal cardinality in a solvable group

In this paper two algorithms are presented which compute a set of generators of minimal cardinality for a finite soluble group given by a polycyclic presentation. The first can be used when a chief series is available. The second algorithm is less simple, but nevertheless efficient, and can be used when it is difficult or too expensive to compute a chief series. The problem of determining the minimal number d (G) of generators when G is a solvable group has been discussed and solved by Gaschütz, and the ideas for these algorithms are essentially suggested by the work of Gaschütz. In the Appendices CAYLEY V.3.7.2 procedures are listed.