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Dear GAP Forum,

A small addendum to Eamonn's message.

Eamonn's method produces as output a group with 14 generators. Ella Shelev

originally asked for the Burnside group as a finitely-presented group with

four generators. This can be achieved using the Tietze transformation package

in GAP as follows:

gap> b := Pq(f,"Prime",3,"Exponent",3,"ClassBound",3); Group( G.1, G.2, G.3, G.4, G.5, G.6, G.7, G.8, G.9, G.10, G.11, G.12, G.13, G.14 ) gap> g := FpGroup(b); Group( G.1, G.2, G.3, G.4, G.5, G.6, G.7, G.8, G.9, G.10, G.11, G.12, G.13, G.\ 14 ) gap> p := PresentationFpGroup(g); << presentation with 14 gens and 105 rels of total length 428 >> gap> SimplifyPresentation(p); #I there are 11 generators and 95 relators of total length 509 #I there are 7 generators and 71 relators of total length 545 #I there are 5 generators and 61 relators of total length 660 #I there are 4 generators and 58 relators of total length 778 #I there are 4 generators and 58 relators of total length 752 gap> h := FpGroupPresentation(p); Group( G.1, G.2, G.3, G.4 ) gap>

Steve

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