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Finite groups have short rewriting systems. (English) Zbl 1214.20036
Kappe, Luise-Charlotte (ed.) et al., Computational group theory and the theory of groups. II. Papers of the conference on computational group theory and cohomology, Harlaxton College, Grantham, UK, August 4–8, 2008 and the AMS special session on computational group theory, Western Michigan University, Kalamazoo, MI, USA, October 17–19, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4805-0/pbk). Contemporary Mathematics 511, 185-200 (2010).
Summary: All but finitely many finite groups have a rewriting system whose number of rules is less than the square root of the group order. A natural rewriting system is given for finite groups of Lie type.
For the entire collection see [Zbl 1186.20002].

MSC:
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
68Q42 Grammars and rewriting systems
20D06 Simple groups: alternating groups and groups of Lie type
20F05 Generators, relations, and presentations of groups
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