Application of Computers to Questions like those of Burnside, II

We show how automorphisms can be used to reduce signiicantly the resources needed to enforce laws in p-groups. This increases the extent to which Burnside groups with prime-power exponent can be studied in detail. For example, we describe how to construct power-conjugate presentations for the restricted Burnside groups R(5; 4) and R(3; 5) which have orders 2 2728 and 5 2282 respectively. We also describe how to determine the exponent of a p-group and report on relevant features of the current implementation of an algorithm to compute power-conjugate presentations.