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Dear Roger Beresford,

let me try to answer to your first question.

(1) How can I extract the defining relationships for a group from GAP? =

Using gmmnn as shorthand for SmallGroup(mm,nn), I particularly need them =

for g2003, g2704, fifteen of the 32-element groups, g3603, & g3609.

For example, let us take the first group you need:

gap> G:=SmallGroup(20,03); <pc group of size 20 with 3 generators>

BTW, with SmallGroup you obtain a group which is given by

power-commutator presentation, so its generating system is not

necessary the minimal one:

gap> MinimalGeneratingSet(G);

[ f1, f3 ]

To get relations, first we construct an isomorphic finitely presented

group:

gap> f:=IsomorphismFpGroup(G); [ f1, f2, f3 ] -> [ F1, F2, F3 ] gap> H:=Image(f); <fp group of size 20 on the generators [ F1, F2, F3 ]>

And now you could see relations:

gap> RelatorsOfFpGroup(H); [ F1^2*F2^-1, F2^-1*F1^-1*F2*F1, F3^-1*F1^-1*F3*F1*F3^-1, F2^2, F3^-1*F2^-1*F3*F2*F3^-3, F3^5 ]

Sincerely yours,

Alexander Konovalov

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