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