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Dear GAP Forum

I am trying to create the burnside group of exponent 3 and 4 generators.

According to P.Hall the elements of this group can all be written in the

form:

a^i1*b^i2*c^i3*d^i4*Comm(a,b)^i5*Comm(a,c)^i6*Comm(a,d)^i7*Comm(b,c)^i8* Comm(b,d)^i9*Comm(c,d)^i10*Comm(Comm(a,b),c)^i11*Comm(comm(a,b),d)^i12* Comm(Comm(a,c),d)^i13*Comm(Comm(b,c),d)^i14

Where a,b,c,d are the generators and

0 <= i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14 <= 3

The size of this group is 3^14.

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?

Best Regards

Ella Shalev

Tel-Aviv university.

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