Newman, M. F.; O’Brien, E. A. Application of computers to questions like those of Burnside. II. (English) Zbl 0867.20003 Int. J. Algebra Comput. 6, No. 5, 593-605 (1996). [For Part I, cf. G. Havas and M. F. Newman, Lect. Notes Math. 806, 211-230 (1980; Zbl 0432.20033).]We show how automorphisms can be used to reduce significantly 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. Reviewer: M.F.Newman (Canberra) Cited in 1 ReviewCited in 22 Documents MSC: 20-04 Software, source code, etc. for problems pertaining to group theory 20D15 Finite nilpotent groups, \(p\)-groups 20F05 Generators, relations, and presentations of groups 20F12 Commutator calculus 20F50 Periodic groups; locally finite groups 20F14 Derived series, central series, and generalizations for groups 20F45 Engel conditions Keywords:enforcing exponent laws; automorphisms; laws in \(p\)-groups; power-conjugate presentations; restricted Burnside groups; algorithms Citations:Zbl 0432.20033 Software:Cayley; QUOTPIC PDFBibTeX XMLCite \textit{M. F. Newman} and \textit{E. A. O'Brien}, Int. J. Algebra Comput. 6, No. 5, 593--605 (1996; Zbl 0867.20003) Full Text: DOI Online Encyclopedia of Integer Sequences: Order of Burnside group B(3,n) of exponent 3 and rank n. Order of Burnside group B(4,n) of exponent 4 and rank n.