[GAP Forum] something wrong with NewmanInfinityCriterion?

[Alexander Hulpke]

Dear Lev Glebsky,

Thank you very much for this bug report. It was prompted by a misprint in a book and will be fixed in the next release of GAP.

Regards,

   Alexander Hulpke


On Apr 8, 2013, at 4/8/13 12:11, glebsky at cactus.iico.uaslp.mx wrote:

> Well.. It is known that the groups
> M(a,b,c)=<x,y,z | x^y=x^a, y^z=y^b, z^x=z^b> are finite (see for example
> D.L. Johnson Presentations of groups, Ch.7, exercise 16).
> (Here a,b,c are natural numbers, x^y=y^(-1)*x*y.)
> 
> But running
> GAP (inside SAGE) I have got:
> 
> sage: f:=FreeGroup("a","b","c");
> sage:
> G:=f/[f.2^-1*f.1*f.2*f.1^-4,f.3^-1*f.2*f.3*f.2^-4,f.1^-1*f.3*f.1*f.3^-4];
> <free group on the generators [ a, b, c ]>
> <fp group on the generators [ a, b, c ]>
> sage: AbelianInvariants(G);
> [ 3, 3, 3 ]
> sage: NewmanInfinityCriterion(G,3)
> true
> 
> Looks wrong?  As far as I understand, passing  NewmanInfinityCriterion(G,3)
> meens that G has arbitrary large homomorphic images in 3-groups. It seems
> to contradict with the following (G is the same as above):
> 
> sage: G3:=PQuotient(G,3);
> sage: h3:=EpimorphismQuotientSystem(G3);
> <3-quotient system of 3-class 4 with 9 generators>
> [ a, b, c ] -> [ a1, a2, a3 ]
> sage: G3:=Image(h3)
> <pc group of size 19683 with 9 generators>
> 
> I am new user of the GAP. I starting to play with a GAP inside SAGE, 4.4.2,
> 
>                                                        Lev.
> 
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