Fix a rare error message in isomorphism test

lib/autsr.gi

@@ -1015,7 +1015,7 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
           for j in b do
             N:=ClosureSubgroup(N,b);
           od;
-          # insert
+          # insert in series
           for j in [Length(ser),Length(ser)-1..i+1] do
             ser[j+1]:=ser[j];
           od;
@@ -1034,13 +1034,13 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
             Info(InfoMorph,2,"insert2");
           fi;
           N:=ser[i+1]; # the added normal
-          if rada<>fail
-             and ForAny(GeneratorsOfGroup(rada),x->N<>Image(x,N)) then
-            Info(InfoMorph,3,"radical automorphism stabilizer");
-            SetIsGroupOfAutomorphismsFiniteGroup(rada,true);
-            NiceMonomorphism(rada:autactbase:=fail,someCharacteristics:=fail);
-            rada:=Stabilizer(rada,N,asAutom);
-          fi;
+        fi;
+        if rada<>fail
+            and ForAny(GeneratorsOfGroup(rada),x->N<>Image(x,N)) then
+          Info(InfoMorph,3,"radical automorphism stabilizer");
+          SetIsGroupOfAutomorphismsFiniteGroup(rada,true);
+          NiceMonomorphism(rada:autactbase:=fail,someCharacteristics:=fail);
+          rada:=Stabilizer(rada,N,asAutom);
         fi;
       fi;
     until split or fratsim;
@@ -1332,7 +1332,6 @@ local ff,r,d,ser,u,v,i,j,k,p,bd,e,gens,lhom,M,N,hom,Q,Mim,q,ocr,split,MPcgs,
           # move back to bad degree
           rada:=Group(List(GeneratorsOfGroup(rada),
             x-> InducedAutomorphism(InverseGeneralMapping(ind),x)));
-
         fi;
       fi;
 

lib/ctblfuns.gd

@@ -1013,7 +1013,7 @@ DeclareAttribute( "TrivialCharacter", IsGroup );
 ##  gap> NaturalCharacter( Group( [ [ 0, -1 ], [ 1, -1 ] ] ) );
 ##  Character( CharacterTable( Group([ [ [ 0, -1 ], [ 1, -1 ] ] ]) ),
 ##  [ 2, -1, -1 ] )
-##  gap> d8:= DihedralGroup( 8 );;  hom:= IsomorphismPermGroup( d8 );;
+##  gap> d8:= DihedralGroup( 8 );;  hom:= RegularActionHomomorphism( d8 );;
 ##  gap> NaturalCharacter( hom );
 ##  Character( CharacterTable( <pc group of size 8 with 3 generators> ),
 ##  [ 8, 0, 0, 0, 0 ] )

lib/ctblgrp.gi

@@ -82,6 +82,7 @@ local D,C,cl,pl;
   D.classes:= ConjugacyClasses( C );
   cl:=ShallowCopy(D.classes);
   D.classreps:=List(cl,Representative);
+  D.centfachom:=[];
   D.klanz:=Length(cl);
   D.classrange:=[1..D.klanz];
   Info(InfoCharacterTable,1,D.klanz," classes");
@@ -1727,7 +1728,23 @@ DoubleCentralizerOrbit := function(D,c1,c2)
   else
     #Info(InfoCharacterTable,3,"using DoubleCosets;");
     cent:=Centralizer(D.classes[inv]);
-    l:=DoubleCosetRepsAndSizes(D.group,cent,Centralizer(D.classes[c2]));
+    if IndexNC(D.group,cent)<=10^5 then
+      if not IsBound(D.centfachom[inv]) then
+        e:=ActionHomomorphism(D.group,RightTransversal(D.group,cent),OnRight,
+          "surjective");
+        Image(e);
+        # do not use action later on
+        e:=AsGroupGeneralMappingByImages(e);
+        D.centfachom[inv]:=e;
+      else
+        e:=D.centfachom[inv];
+      fi;
+      s:=Orbits(Image(e,Centralizer(D.classes[c2])),[1..IndexNC(D.group,cent)]);
+      l:=List(s,x->[PreImagesRepresentative(e,
+        RepresentativeAction(Image(e),1,x[1])),Size(cent)*Length(x)]);
+    else
+      l:=DoubleCosetRepsAndSizes(D.group,cent,Centralizer(D.classes[c2]));
+    fi;
     s1:=Size(cent);
     e:=[];
     s:=[];

lib/factgrp.gd

@@ -232,11 +232,12 @@ DeclareSynonym( "ImproveOperationDegreeByBlocks",
 ##  called internally might try a degree reduction.)
 ##  <P/>
 ##  <Example><![CDATA[
+##  gap> iso:=RegularActionHomomorphism(SymmetricGroup(4));;
 ##  gap> image:= Image( iso );;  NrMovedPoints( image );
 ##  24
 ##  gap> small:= SmallerDegreePermutationRepresentation( image );;
 ##  gap> Image( small );
-##  Group([ (2,3), (1,2,3), (1,3)(2,4), (1,2)(3,4) ])
+##  Group([ (2,5,4,3), (1,4)(2,6)(3,5) ])
 ##  gap> g:=Image(IsomorphismPermGroup(GL(4,5)));;
 ##  gap> sm:=SmallerDegreePermutationRepresentation(g:cheap);;
 ##  gap> NrMovedPoints(Range(sm));

lib/factgrp.gi

@@ -266,6 +266,10 @@ local pool,p,h,ise,emb,i,j;
         fi;
       od;
       ise:=List(ise,i->GetNaturalHomomorphismsPool(G,pool.ker[i]));
+      if not (ForAll(ise,IsPcGroup) or ForAll(ise,IsPermGroup)) then
+        ise:=List(ise,x->x*IsomorphismPermGroup(Image(x)));
+      fi;
+
       h:=CallFuncList(DirectProduct,List(ise,Image));
       emb:=List([1..Length(ise)],i->Embedding(h,i));
       emb:=List(GeneratorsOfGroup(G),

lib/fitfree.gd

@@ -141,6 +141,7 @@ InstallTrueMethod(CanComputeFittingFree,HasFittingFreeLiftSetup);
 ##  </ManSection>
 ##  <#/GAPDoc>
 DeclareGlobalFunction("FittingFreeSubgroupSetup");
+DeclareOperation("DoFFSS",[IsGroup,IsGroup]);
 
 # This attribute is used for groups treated by constructive recognition and
 # a composition tree. It is declared in the library such that the function

lib/fitfree.gi

@@ -41,21 +41,11 @@ local R;
   fi;
 end);
 
-InstallGlobalFunction(FittingFreeSubgroupSetup,function(G,U)
-local cache,ffs,pcisom,rest,it,kpc,k,x,ker,r,pool,i,xx,inv,pregens;
-  ffs:=FittingFreeLiftSetup(G);
+InstallMethod(DoFFSS,"generic",IsIdenticalObj,[IsGroup and IsFinite,IsGroup],0,
+function(G,U)
+local ffs,pcisom,rest,it,kpc,k,x,ker,r,pool,i,xx,inv,pregens,iso;
 
-  # result cached?
-  if not IsBound(U!.cachedFFS) then
-    cache:=[];
-    U!.cachedFFS:=cache;
-  else
-    cache:=U!.cachedFFS;
-  fi;
-  r:=First(cache,x->IsIdenticalObj(x[1],ffs));
-  if r<>fail then
-    return r[2];
-  fi;
+  ffs:=FittingFreeLiftSetup(G);
 
   pcisom:=ffs.pcisom;
 
@@ -90,25 +80,51 @@ local cache,ffs,pcisom,rest,it,kpc,k,x,ker,r,pool,i,xx,inv,pregens;
     k:=ffs.pcgs;
   else
 
-    inv:=RestrictedInverseGeneralMapping(rest);
-    pregens:=List(SmallGeneratingSet(Image(rest)),
-      x->ImagesRepresentative(inv,x));
-    it:=CoKernelGensIterator(inv);
-    kpc:=TrivialSubgroup(Image(pcisom));
-    while not IsDoneIterator(it) do
-      x:=NextIterator(it);
-      pool:=[x];
-      for x in pool do
-        xx:=ImagesRepresentative(pcisom,x);
-        if not xx in kpc then
-          kpc:=ClosureGroup(kpc,xx);
-          for i in pregens do
-            Add(pool,x^i);
-          od;
+    iso:=IsomorphismFpGroup(Image(rest,U));
+    pregens:=List(GeneratorsOfGroup(Range(iso)),x->
+      PreImagesRepresentative(rest,PreImagesRepresentative(iso,x)));
+    # evaluate relators
+    pool:=List(RelatorsOfFpGroup(Range(iso)),
+      x->MappedWord(x,FreeGeneratorsOfFpGroup(Range(iso)),pregens));
+    # divide off original generators
+    Append(pool,List(GeneratorsOfGroup(U),x->x/
+      MappedWord(UnderlyingElement(ImagesRepresentative(iso,ImagesRepresentative(ffs.factorhom,x))),FreeGeneratorsOfFpGroup(Range(iso)),pregens)));
+
+
+    pool:=List(pool,x->ImagesRepresentative(pcisom,x));
+    kpc:=SubgroupNC(Image(pcisom),pool);
+    pool:=List(SmallGeneratingSet(kpc),x->PreImage(pcisom,x));
+    # normal closure
+    for x in pool do
+      for i in GeneratorsOfGroup(U) do
+        xx:=x^i;
+        k:=ImagesRepresentative(pcisom,xx);
+        if not k in kpc then
+          kpc:=ClosureSubgroupNC(kpc,k);
+          Add(pool,xx);
         fi;
       od;
-      #Print("|pool|=",Length(pool),"\n");
     od;
+
+#    inv:=RestrictedInverseGeneralMapping(rest);
+#    pregens:=List(SmallGeneratingSet(Image(rest)),
+#      x->ImagesRepresentative(inv,x));
+#    it:=CoKernelGensIterator(inv);
+#    kpc:=TrivialSubgroup(Image(pcisom));
+#    while not IsDoneIterator(it) do
+#      x:=NextIterator(it);
+#      pool:=[x];
+#      for x in pool do
+#       xx:=ImagesRepresentative(pcisom,x);
+#       if not xx in kpc then
+#         kpc:=ClosureGroup(kpc,xx);
+#         for i in pregens do
+#           Add(pool,x^i);
+#         od;
+#       fi;
+#      od;
+#      #Print("|pool|=",Length(pool),"\n");
+#    od;
     SetSize(U,Size(Image(rest))*Size(kpc));
     k:=InducedPcgs(FamilyPcgs(Image(pcisom)),kpc);
     k:=List(k,x->PreImagesRepresentative(pcisom,x));
@@ -131,6 +147,44 @@ local cache,ffs,pcisom,rest,it,kpc,k,x,ker,r,pool,i,xx,inv,pregens;
             pcgs:=k,
             serdepths:=List(ffs.depths,y->First([1..Length(r)],x->r[x]>=y))
             );
+
+  return r;
+
+end);
+
+InstallGlobalFunction(FittingFreeSubgroupSetup,function(G,U)
+local ffs,cache,rest,ker,k,r;
+  ffs:=FittingFreeLiftSetup(G);
+
+  # result cached?
+  if not IsBound(U!.cachedFFS) then
+    cache:=[];
+    U!.cachedFFS:=cache;
+  else
+    cache:=U!.cachedFFS;
+  fi;
+  r:=First(cache,x->IsIdenticalObj(x[1],ffs));
+  if r<>fail then
+    return r[2];
+  fi;
+
+  if IsIdenticalObj(G,U) or GeneratorsOfGroup(G)=GeneratorsOfGroup(U) then
+    rest:=ffs.factorhom;
+    ker:=ffs.radical;
+    k:=ffs.pcgs;
+    r:=[1..Length(k)];
+    r:=rec(parentffs:=ffs,
+              rest:=rest,
+              ker:=ker,
+              pcgs:=k,
+              serdepths:=List(ffs.depths,y->First([1..Length(r)],x->r[x]>=y))
+              );
+  else
+    r:=DoFFSS(G,U);
+  fi;
+
+  k:=r.pcgs;
+  rest:=r.rest;
   Add(cache,[ffs,r]); # keep
   if Length(k)=0 then
     SetSize(U,Size(Image(rest)));

lib/ghom.gd

@@ -673,3 +673,5 @@ DeclareAttribute( "ImagesSmallestGenerators",
 ##  <#/GAPDoc>
 ##
 DeclareAttribute( "RegularActionHomomorphism", IsGroup );
+
+DeclareGlobalName("IsomorphismAbelianGroupViaIndependentGenerators");

lib/ghom.gi

@@ -1397,6 +1397,10 @@ function ( G )
   if not HasIsAbelian( G ) and IsAbelian( G ) then
     # Redispatch to give the special methods for abelian groups a chance.
     return IsomorphismPermGroup( G );
+  elif (not HasIsSolvableGroup(G)) and IsSolvableGroup(G) then
+    # Redispatch to give the special methods for solvable groups a chance.
+    return IsomorphismPermGroup( G );
+
     # MH: Disabled the following code for now, as computing IsNilpotentGroup
     # can be very expensive, depending on the group type. We could
     # re-enable it for e.g. pc groups, but I am not sure whether it is

lib/grp.gd

@@ -4279,10 +4279,9 @@ DeclareAttribute( "IsomorphismSpecialPcGroup", IsGroup );
 ##  gap> g:=SmallGroup(24,12);
 ##  <pc group of size 24 with 4 generators>
 ##  gap> iso:=IsomorphismPermGroup(g);
-##  <action isomorphism>
+##  [ f1, f2, f3, f4 ] -> [ (2,3), (2,3,4), (1,2)(3,4), (1,3)(2,4) ]
 ##  gap> Image(iso,g.3*g.4);
-##  (1,12)(2,16)(3,19)(4,5)(6,22)(7,8)(9,23)(10,11)(13,24)(14,15)(17,
-##  18)(20,21)
+##  (1,4)(2,3)
 ##  ]]></Example>
 ##  <P/>
 ##  In many cases the permutation representation constructed by