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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
Cayley; QUOTPIC
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