Dear Gap-forum,
using the most recent version of GAP (under UNIX), the program below
yields, after some successful runs even over the innermost
`for'-loops, the following message I don't understand what it comes
from and what it is supposed to tell me.
By the way, I found no smaller group than the Mathieu group M_24
producing this phenomenon.
Peter ---------------------------------------------------------------- OrbRep:=function(g,s) return List(Orbits(g,s),x->x[1]); end; g:=PrimitiveGroup(24,3);# M24 cg:=Filtered(ConjugacyClasses(g),x->Size(x)>1 and not IsAbelian(Centralizer(g,Representative(x)))); Sort(cg,function(v,w) return Size(v)>Size(w);end); Print(g,"\n"); for ca in cg do a:=Representative(ca); ca:=Centralizer(g,a); cca:=Filtered(ConjugacyClasses(ca),x->Size(x)>1 and not IsAbelian(Centralizer(g,Representative(x)))); Sort(cca,function(v,w) return Size(v)>Size(w);end); for cclass in cca do c:=Representative(cclass); if not c in Subgroup(g,[a]) then for d in Difference(OrbRep(Centralizer(ca,c),Elements(cclass)), Subgroup(g,[a,c])) do if c*d*c=d*c*d then h3:=Subgroup(g,[a,c,d]); for b in Difference(OrbRep(Centralizer(g,h3), Elements(ConjugacyClass(Centralizer(g,d),a))),h3) do if a*b*a=b*a*b and b*c*b*c=c*b*c*b then h:=Subgroup(g,[a,b,c,d]); Print(Order(g,a)," ",Order(g,c)," ",Size(h),"\n"); fi; od; fi; od; fi; od; od; ---------------------------------------------------------------- gap> Read("F4"); M(24) 7 2 1008 7 2 1008 5 3 720 ... (many lines deleted) 3 3 576 3 4 288 3 2 72 Error, Record: element 'fusingElement' must have an assigned value at fusingElement := power.fusingElement ^ (Size( power.galoisGroup ) / (sizeKnownPart * div[i])) ... in CompleteGaloisGroupPElement( G, rationalClasses[j], rationalClasses[j].powers[p], p ) called from RationalClassesPElements( G, p ) called from RationalClassesPermGroup( G ) called from G.operations.RationalClasses( G ) called from RationalClasses( G ) called from ... brk> quit; gap> quit;