Computing Character Degrees in p-Groups

This paper presents a reeursive procedure for computing the degrees of the irreducible complex characters of a finite p-group by working up a central series in the group. A program written in the computer group theory language CAVLE7 is presented which implements this algorithm assuming that the p-group is given in terms of a power-commutator presentation. Some times for sample runs are presented which indicate that the CAYLEY implementation is effective for groups of order up to p^1^5 for small primes. In particular, this approach seems to produce the character degrees much faster than using CAYLEY,''S built-in character table function and reading off the degrees.