Computing a set of generators of minimal cardinality in a solvable group (Q1333156)

Using ideas of \textit{W. Gaschütz} [Ill. J. Math. 3, 469-476 (1959; Zbl 0093.25002)] two algorithms are presented, which compute a set of generators of minimal cardinality for finite soluble groups. The groups in question are given by a polycyclic presentation. The first algorithm is designed to be used when a chief series is available in advance. The second algorithm is more involved, but it can be used with efficiency in the absence of a chief series, or when such a chief series is expensive to compute.