Dear Forum,
in his recent message to the forum, Mark Lewis described a problem computing=
with Ag groups obtained via AgGroupFpGroup from a finitely presented group.=
=20
His problem is due to the fact that the particular Ag representation is not=
*consistent*; as the section about "AgGroupFpGroup" in the GAP manual=
points out, this may lead to wrong computations; as it seems, it may also=
lead to runtime errors.
Try the following:
gap> c := AbstractGenerator ("c");; gap> d := AbstractGenerator ("d");; gap> a1 := AbstractGenerator ("a1");; gap> a2 := AbstractGenerator ("a2");; gap> b1 := AbstractGenerator ("b1");; gap> b2 := AbstractGenerator ("b2");; gap>=20 gap> #construct Mark's group gap> g3 := AgGroupFpGroup( rec( =20 > 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)])); Group( d, c, a1, a2, b1, b2 ) gap>=20 gap> # now construct Mark's group as a Fp group gap> fp3 := Group (d,c,a1,a2,b1,b2); Group( d, c, a1, a2, b1, b2 ) gap> fp3.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)];; gap> IsConsistent (g3); false # this is the reason for the trouble gap> Size (g3); Size (fp3); 96 # so GAP even gets the size wrong 24
Note that CharTable (fp3) works without problems, and returns the correct=
result within seconds (on any reasonably fast machine). fp3 is, of course,=
isomorphic with S4.=20
Hope this helps,
Burkhard.