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Application of computers to questions like those of Burnside. II. (English) Zbl 0867.20003
[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.

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
Software:
Cayley; QUOTPIC
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