Dear GAP Forum,
Mark L. Lewis wrote about a problem with the computation of a character
table of a group.
I load in a file with the following group.
c := AbstractGenerator ("c"); d := AbstractGenerator ("d"); a1 := AbstractGenerator ("a1"); a2 := AbstractGenerator ("a2"); b1 := AbstractGenerator ("b1"); b2 := AbstractGenerator ("b2"); g3 := AgGroupFpGroup( rec( generators := [d,c,a1,a2,b1,b2], relators := [b1^2,b2^2,a1^2*(b1)^(-1),a2^2*(b2)^(-1),c^3,d^2, (a1^c)*(a2)^(-1),(a2^c)*(a1*a2)^(-1), (b1^c)*(b2)^(-1),(b2^c)*(b1*b2)^(-1), (c^d)*(c^2)^(-1), (a2^d)*(a1*a2)^(-1),(b2^d)*(b1*b2)^(-1)]));This group seems to load ok, but when I ask GAP to compute the character
table of g3, I get the following response.
...
The problem is that the given presentation for `g3' is not consistent
as a presentation of a solvable group with composition length 6.
To see this, we use the ``clean'' way to define a finitely presented
group, and ask for the size.
gap> f:= FreeGroup( 6 );; gap> c := f.1;; gap> d := f.2;; gap> a1 := f.3;; gap> a2 := f.4;; gap> b1 := f.5;; gap> b2 := f.6;; gap> gap> g3:= g / [b1^2,b2^2,a1^2*(b1)^(-1),a2^2*(b2)^(-1),c^3,d^2, gap> (a1^c)*(a2)^(-1),(a2^c)*(a1*a2)^(-1), gap> (b1^c)*(b2)^(-1),(b2^c)*(b1*b2)^(-1), gap> (c^d)*(c^2)^(-1), gap> (a2^d)*(a1*a2)^(-1),(b2^d)*(b1*b2)^(-1)];; gap> Size( g3 ); 24
Kind regards
Thomas