TWOCOHOM: Added tests: Construction of perfect groups

Includes action of compatible pairs on cohomology group and model.

lib/twocohom.gi

@@ -900,8 +900,6 @@ local field,fp,fpg,gens,hom,mats,fm,mon,kb,tzrules,dim,rules,eqs,i,j,k,l,o,l1,
  return a;
  end;
 
- onemat:=One(mo.generators[1]);
- zerovec:=Zero(onemat[1]);
  # matrix corresponding to monoid word
  mapped:=function(list)
  local a,i;
@@ -1072,6 +1070,7 @@ local field,fp,fpg,gens,hom,mats,fm,mon,kb,tzrules,dim,rules,eqs,i,j,k,l,o,l1,
  x->ImagesRepresentative(m,
  PreImagesRepresentative(fm,x))); #Elements for monoid generators
  pre:=mats;
+ onemat:=One(G);
  for i in [1..Length(hastail)] do
  r:=rules[hastail[i]];
  m:=LeftQuotient(mapped(r[2]),mapped(r[1]));
@@ -1080,6 +1079,9 @@ local field,fp,fpg,gens,hom,mats,fm,mon,kb,tzrules,dim,rules,eqs,i,j,k,l,o,l1,
  od;
  fi;
 
+ onemat:=One(mo.generators[1]);
+ zerovec:=Zero(onemat[1]);
+
  mats:=List(GeneratorsOfMonoid(mon),
  x->ImagesRepresentative(hom,PreImagesRepresentative(fp,
  PreImagesRepresentative(fm,x)))); # matrices for monoid generators

tst/testextra/makeperfect.g

@@ -0,0 +1,81 @@
+# construct perfect groups of given order
+
+Practice:=function(n) #makes perfect
+local isot,res,resp,d,i,j,nt,p,e,q,cf,m,coh,v,new,quot,nts,pf,pl,comp,reps;
+ isot:=function(g,h)
+ local c,d;
+ if Collected(List(ConjugacyClasses(g),
+ x->[Order(Representative(x)),Size(x)]))<>
+ Collected(List(ConjugacyClasses(h),
+ x->[Order(Representative(x)),Size(x)])) then return false;
+ fi;
+ if Collected(List(MaximalSubgroupClassReps(g),Size))<>
+ Collected(List(MaximalSubgroupClassReps(h),Size)) then return false;
+ fi;
+ if Collected(List(NormalSubgroups(g),
+ x->[Size(x),IsAbelian(x),Size(Centralizer(g,x))]))<>
+ Collected(List(NormalSubgroups(h),
+ x->[Size(x),IsAbelian(x),Size(Centralizer(h,x))])) then return false;
+ fi;
+ c:=CharacterTable(g);;Irr(c);
+ d:=CharacterTable(h);;Irr(d);
+ if TransformingPermutationsCharacterTables(c,d)=fail then return false;fi;
+ return IsomorphismGroups(g,h)<>fail;
+ end;
+
+ res:=[];
+ resp:=[];
+ d:=Filtered(DivisorsInt(n),x->x<n);
+ for i in d do
+ nts:=n/i;
+ if IsPrimePowerInt(nts) then
+ p:=Factors(nts)[1];
+ e:=LogInt(nts,p);
+ pl:=[];
+ for j in [1..NrPerfectGroups(i)] do
+ q:=PerfectGroup(IsPermGroup,i,j);
+ new:=Name(q);
+ q:=Group(SmallGeneratingSet(q));
+ SetName(q,new);
+ Add(pl,q);
+ od;
+ for j in [1..Length(pl)] do
+ q:=pl[j];
+ #Print("Using ",i,", ",j,": ",q,"\n");
+ cf:=IrreducibleModules(q,GF(p),e)[2];
+ cf:=Filtered(cf,x->x.dimension=e);
+ for m in cf do
+ #Print("Module dimension ",m.dimension,"\n");
+ coh:=TwoCohomologyGeneric(q,m);
+
+ comp:=CompatiblePairs(q,m);
+ reps:=CompatiblePairOrbitRepsGeneric(comp,coh);
+ for v in reps do
+ new:=FpGroupCocycle(coh,v,true);
+ if IsPerfect(new) then
+ # could it have been gotten in another way?
+ pf:=Image(IsomorphismPermGroup(new));
+ nt:=NormalSubgroups(pf);
+ if ForAll(nt,x->Size(x)=1 or Size(x)>=nts) then
+ nt:=Filtered(nt,x->Size(x)=nts);
+ if (not ForAny(List(nt,x->pf/x),x->ForAny([1..j-1],y->
+ isot(pl[y],x)))) and ForAll(resp,
+ x->isot(x,Image(IsomorphismPermGroup(new)))=false) then
+ Add(res,new);
+ Add(resp,Image(IsomorphismPermGroup(new)));
+ #Print("found nr. ",Length(res),"\n");
+ else
+ #Print("smallerb\n");
+ fi;
+ #else Print("smallera\n");
+ fi;
+ fi;
+ od;
+
+ od;
+ od;
+ fi;
+ od;
+ return res;
+end;
+

tst/testextra/perfect.tst

@@ -0,0 +1,13 @@
+#############################################################################
+##
+## Test for cohomology and isomorphism: Recompute perfect groups
+##
+gap> START_TEST("perfect.tst");
+gap> READ_GAP_ROOT("tst/testextra/makeperfect.g");;
+gap> l:=Practice(1920);;
+gap> Length(l);
+7
+gap> l:=Practice(10752);;
+gap> Length(l);
+9
+gap> STOP_TEST( "perfect.tst", 1);

tst/testinstall/twocohom.tst

@@ -0,0 +1,25 @@
+gap> START_TEST("twocohom.tst");
+gap> g:=PerfectGroup(IsPermGroup,1344,1);;
+gap> mo:=IrreducibleModules(g,GF(2),1);;List(mo[2],x->x.dimension);
+[ 1 ]
+gap> mo:=IrreducibleModules(g,GF(2),0);;List(mo[2],x->x.dimension);
+[ 1, 3, 3, 8 ]
+gap> coh:=TwoCohomologyGeneric(g,mo[2][2]:
+> model:=PerfectGroup(IsPermGroup,10752,1));;
+gap> Length(coh.cohomology);
+2
+gap> comp:=CompatiblePairs(g,mo[2][2]);
+<group of size 2688 with 5 generators>
+gap> reps:=CompatiblePairOrbitRepsGeneric(comp,coh);;Length(reps);
+3
+gap> h:=FpGroupCocycle(coh,reps[1],true);;
+gap> h:=Image(IsomorphismPermGroup(h));;
+gap> Collected(List(MaximalSubgroupClassReps(h),Size));
+[ [ 1344, 7 ], [ 1536, 2 ] ]
+gap> h:=FpGroupCocycle(coh,reps[2],true);;
+gap> h:=Image(IsomorphismPermGroup(h));;
+gap> Collected(List(MaximalSubgroupClassReps(h),Size));
+[ [ 1344, 3 ], [ 1536, 2 ] ]
+
+# that's all, folks
+gap> STOP_TEST( "twocohom.tst", 1);