[GAP Forum] Simplifying presentations of abelian groups

Martin Jones m.s.jones at newcastle.ac.uk
Mon Apr 21 15:56:41 BST 2008


This is my first question. I hope it's not a stupid one. I have an
finitely presented abelian group and I want to obtain a simple
presentation for the group. The command SimplifedFpGroup is not working
satisfactorily (possibly because it doesn't introduce new generators).
How can I make GAP use the fact that the group is abelian and use an
appropriate method?

I'll give an example:
<fp group on the generators [ f1, f2, f3, f4, f5, f6, f7, f8, f9, f10,
  f12, f13, f14, f15, f16 ]>
           (this is my initial group)
<fp group on the generators [ f1, f2, f5, f6 ]>
           (okay, a bit simpler)
[ f1*f2*f1^-1*f2^-1, f2^-1*f5^-1*f2*f5, f1^-1*f6^-1*f1*f6,
  f2^-1*f6^-1*f2*f6, f1^-1*f5^-1*f1*f5, f1*f2^3*f1*f2*f1^2 ]
           (6 commutators and a relation of length 8)
true                       (so it knows it's abelian)
[ 0, 0, 0, 4 ]

In this case what I am looking for is a presentation with 4 generators,
three torsion-free and one of order 4, in terms of the original
generators of G.

Thanks in advance,

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