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#@local c2,e,f,g,gg,i,k,l,n,t,a,b
gap> START_TEST("xgap.tst");
gap> f := FreeGroup(2);
<free group on the generators [ f1, f2 ]>
gap> FactorGroup(f,f);
Group(())
gap> Size(last);
1
gap> f := FreeGroup( "a", "b" );; a := f.1;; b := f.2;;
gap> c2 := f / [ a*b*a^-2*b*a/b, (b^-1*a^3*b^-1*a^-3)^2*a ];;
gap> e := GQuotients(c2,PSL(2,11));;
gap> Length(e);
1
gap> e := e[1];;
gap> i := Image(e);;
gap> Stabilizer(i,1);;
gap> g := PreImage(e,last);;
gap> l := LowIndexSubgroupsFpGroup(g,TrivialSubgroup(g),5);;
gap> Filtered(last,x->IndexInWholeGroup(x)=60);;
gap> gg := last[5];;
gap> n := Normalizer(c2,gg);;
gap> Index(c2,n) = Index(c2,gg);
false
gap> Index(c2,n);
12
gap> Index(c2,gg);
60
gap> k := Kernel(e);;
gap> LowIndexSubgroupsFpGroup(c2,k,11);
[ Group(<fp, no generators known>), Group(<fp, no generators known>),
Group(<fp, no generators known>) ]
gap> Length(last);
3
gap> l := LowIndexSubgroupsFpGroup(c2,TrivialSubgroup(c2),11);;
gap> List(l,x->ConjugacyClassSubgroups(c2,x));;
gap> Length(last);
11
gap> f := FreeGroup(2);
<free group on the generators [ f1, f2 ]>
gap> t := TrivialSubgroup(f);
Group([ ])
gap> CanComputeSize(t);
true
gap> HasSize(t);
true
gap> Size(t);
1
gap> STOP_TEST("xgap.tst");
[ Dauer der Verarbeitung: 0.5 Sekunden
(vorverarbeitet)
]
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