> < ^ Date: Thu, 15 Oct 1998 21:14:15 +0000
^ From: Esteban Crespi <ecv@mail.kubilai.com >
^ Subject: two problems

While trying to find a minimal generating set for several permutation
groups I have repeteadly found the following problem:

gap> G := Group((1,4)(2,6)(3,5),
>                           (1,4)(2,5)(3,6),
>                           (1,3,2)(4,5,6),
>                           (1,2,3)(4,5,6));
Group([ (1,4)(2,6)(3,5), (1,4)(2,5)(3,6), (1,3,2)(4,5,6),
(1,2,3)(4,5,6) ]) 
gap> MinimalGeneratingSet(G); 
Error no method found for operation MinimalGeneratingSet at 
Error( "no method found for operation ", name ); <function>( 
<arguments> )  ...
gap> EulerianFunction(G,2); 
Error no method found for operation EulerianFunction with 2 arguments 
...
gap> Size(G); 
36 
gap> EulerianFunction(G,2); 
216 
gap>MinimalGeneratingSet(G); 
Error no method found for operation 
InducedPcgsByPcSequenceAndGenerators with \ 3 arguments 
...

I suposse this is a bug, (though I am not sure if this is the
correct place to report). I have treated the bugfixes 1 to 4 before
making this test.

Also I don't know if the following code is also a bug or it is simply
not implemented:

gap> G := Group((1,2,3),(1,2));
Group([ (1,2,3), (1,2) ])
gap> F := FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> GQuotients(F,G);
Error argument for `ElementsFamily' must have categories `[
"IsFamily" ]' at Error( "argument for `", name, "' must have
categories `", filt, "'" ); ElementsFamily( RelatorsOfFpGroup( f ) )
called from KernelOfMultiplicativeGeneralMapping( i ) called from
<function>( <arguments> ) called from read-eval-loop

Somebody could tell me of a way around this problem, say, how to find
all epimorphism from a free group onto a permutation group.

Thank you.
Esteban Crespi de Valldaura


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