The p-group generation algorithm

The theory and implementation of an algorithm used in generating descriptions of p-groups aredescribed. Some applications and details of the performance of the algorithm are provided

A computer-based approach to the classification of nilpotent Lie algebras

We adopt the $p$-group generation algorithm to classify small-dimensional nilpotent Lie algebras over small fields. Using an implementation of this algorithm, we list the nilpotent Lie algebras of dimension at most~9 over \F_2 and those of dimension at most~7 over \F_3 and \F_5.Comment: submitte