Dear GAP Forum,

Ella Shalev asks

I am trying to create the burnside group of exponent 3 and 4 generators.
Can someone tell me how can I present it as a Finitely Presented
Group with four generators and relations?
Or even just as a group?

An easy option is to use the ANUPQ package distributed with GAP.

Using the "Pq" function B(3, 4) can be constructed
as an AG-group with a power-commutator presentation.

If you care to, you can use FpGroup to construct
a finite presentation for the group.

gap> RequirePackage ("anupq");
gap> F := FreeGroup (4);
Group( f.1, f.2, f.3, f.4 )
gap> G := 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> H := FpGroup (G);
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 )

Eamonn O'Brien