diff --git a/PLAN.md b/PLAN.md
new file mode 100644
index 000000000..beabcbd20
--- /dev/null
+++ b/PLAN.md
@@ -0,0 +1,6 @@
+CachedSLPToNiceGenerators
+Completely independent implementation. Computes an SLP and maybe also the
+nicegens, then stores it. Then, whenever someone needs another
+SLPToNiceGenerators, this can be taken and evaluated.
+Wherever this is called, assert that this and `CalcNiceGens` return the same
+group elements, maybe even SLPs with equal `LinesOfSLP`.
diff --git a/doc/recognition.xml b/doc/recognition.xml
index 92060023e..c7832939e 100644
--- a/doc/recognition.xml
+++ b/doc/recognition.xml
@@ -264,7 +264,7 @@ returns <K>true</K>.
 </ManSection>
 
 
-The following two attributes are concerned with the relation between
+The following four attributes are concerned with the relation between
 the original generators and the nice generators for a node.
 They are used to transport this information from a successful find
 homomorphism method up to the recursive recognition function:
@@ -272,7 +272,6 @@ homomorphism method up to the recursive recognition function:
 <#Include Label="calcnicegens">
 <#Include Label="CalcNiceGensGeneric">
 <#Include Label="CalcNiceGensHomNode">
-<#Include Label="CalcNiceGens">
 <#Include Label="slptonice">
 
 The following three attributes are concerned with the administration of the
diff --git a/gap/base/recognition.gd b/gap/base/recognition.gd
index cf463517b..1c1fb30c9 100644
--- a/gap/base/recognition.gd
+++ b/gap/base/recognition.gd
@@ -99,23 +99,24 @@ DeclareAttribute( "Homom", IsRecogNode, "mutable" );
 ## <#GAPDoc Label="NiceGens">
 ## <ManSection>
 ## <Attr Name="NiceGens" Arg="ri"/>
+## <Attr Name="NiceGens" Arg="ri, origgens"/>
 ## <Description>
-##     The value of this attribute must be set for all nodes and contains
-##     the nice generators. The <Ref Func="SLPforElement"/> function of the
+##     The value of this attribute contains the nice generators and must be set
+##     for all nodes. The <Ref Func="SLPforElement"/> function of the
 ##     node will write its straight line program in terms of these nice
-##     generators. For leaf nodes, the find homomorphism method is responsible
-##     to set the value of <Ref Attr="NiceGens"/>. By default, the original
-##     generators of the group at this node are taken. For a homomorphism
-##     (or isomorphism), the <Ref Attr="NiceGens"/> will be the concatenation
-##     of preimages of the <Ref Attr="NiceGens"/> of the image group
+##     generators.
+##     <P/>
+##     For a leaf node, <Ref Attr="NiceGens"/> can be any list of generators.
+##     <P/>
+##     For a splitting node, <Ref Attr="NiceGens"/> is the concatenation
+##     of preimages of the <Ref Attr="NiceGens"/> of the factor group
 ##     (see <Ref Attr="pregensfac"/>) and
-##     the <Ref Attr="NiceGens"/> of the kernel. A find homomorphism method
-##     does not have to set <Ref Attr="NiceGens"/> if it finds a homomorphism.
-##     Note however, that such a find homomorphism method has to ensure somehow,
-##     that preimages of the <Ref Attr="NiceGens"/> of the image group
-##     can be acquired. See <Ref Attr="calcnicegens"/>, <Ref Func="CalcNiceGens"/>
-##     and <Ref Attr="slptonice"/>
-##     for instructions.
+##     the <Ref Attr="NiceGens"/> of the kernel.
+##     <P/>
+##     To compute the nice generators, a method with two-arguments is installed
+##     for <Ref Attr="NiceGens"/> which takes the value of the attribute
+##     <Ref Attr="calcnicegens"/> and calls it with the arguments <A>ri</A> and
+##     <A>origgens</A>. For more information see <Ref Attr="calcnicegens"/>.
 ## </Description>
 ## </ManSection>
 ## <#/GAPDoc>
@@ -202,21 +203,30 @@ DeclareAttribute( "validatehomominput", IsRecogNode);
 ## <ManSection>
 ## <Attr Name="calcnicegens" Arg="ri"/>
 ## <Description>
-##     To make the recursion work, we have to acquire preimages of the
-##     nice generators in image groups under the homomorphism found.
-##     But we want to keep the information, how the nice generators
-##     were found, locally at the node where they were found. This
-##     attribute solves this problem of acquiring preimages in the following
-##     way: Its value must be a function, taking the recognition
-##     node <A>ri</A> as first argument, and a list <A>origgens</A> of
-##     preimages of the
-##     original generators of the current node, and has to
-##     return corresponding preimages of the nice generators. Usually this
-##     task can be done by storing a straight line program writing the
-##     nice generators in terms of the original generators and executing
-##     this with inputs <A>origgens</A>. Therefore the default value of
-##     this attribute is the function <Ref Func="CalcNiceGensGeneric"/>
-##     described below.
+##     Stores a function <C>func(ri2, gens2)</C> which computes group elements
+##     of <C>ri2</C> by evaluating words in <C>gens2</C>.
+##     These words must be chosen such that, if <C>ri2</C> is equal to
+##     <A>ri</A> and <C>gens2</C> is equal to
+##     <C>GeneratorsOfGroup(Grp(ri))</C>, then <C>func</C> returns the nice
+##     generators of <A>ri</A>.
+##     Correspondingly, if <C>gens2</C> is another list of group elements, then
+##     the words which yield the nice generators of <A>ri</A> are evaluated in
+##     <C>gens2</C>.
+##     <P/>
+##     This us used by the recursive group recognition to compute preimages of
+##     nice generators as follows:
+##     if <C>imagenode</C> is the image node of a node <C>node</C> and
+##     <C>nodegens</C> are the generators of <C>Grp(node)</C>,
+##     then <C>func(imagenode, nodegens)</C> computes the preimages of the
+##     nice generators of <C>imagenode</C>.
+##     <P/>
+##     Usually <C>func</C> stores a straight line program writing the nice
+##     generators in terms of the generators of the group represented
+##     by <A>ri</A> and executes this with inputs <A>gens2</A>.
+##     <P/>
+##     The default values of this attribute are the functions
+##     <Ref Func="CalcNiceGensGeneric"/> and
+##     <Ref Func="CalcNiceGensHomNode"/>.
 ## </Description>
 ## </ManSection>
 ## <#/GAPDoc>
@@ -547,18 +557,6 @@ DeclareGlobalFunction( "TryFindHomMethod" );
 
 # Helper functions for the generic part:
 
-## <#GAPDoc Label="CalcNiceGens">
-## <ManSection>
-## <Func Name="CalcNiceGens" Arg="ri, origgens"/>
-## <Returns>a list of preimages of the nice generators</Returns>
-## <Description>
-##     This is a wrapper function which extracts the value of the attribute
-##     <Ref Attr="calcnicegens"/> and calls that function with the arguments
-##     <A>ri</A> and <A>origgens</A>.
-## </Description>
-## </ManSection>
-## <#/GAPDoc>
-DeclareGlobalFunction( "CalcNiceGens" );
 DeclareGlobalFunction( "ValidateHomomInput" );
 
 ## <#GAPDoc Label="CalcNiceGensGeneric">
diff --git a/gap/base/recognition.gi b/gap/base/recognition.gi
index 5c4f6057e..1045a9bf8 100644
--- a/gap/base/recognition.gi
+++ b/gap/base/recognition.gi
@@ -23,7 +23,7 @@ RECOG_ViewObj := function( level, ri )
     if IsReady(ri) then
         Print("<recognition node ");
     else
-        Print("<failed recognition node ");
+        Print("<unfinished recognition node ");
     fi;
     if IsBound(ri!.projective) and ri!.projective then
         Print("(projective) ");
@@ -56,7 +56,7 @@ RECOG_ViewObj := function( level, ri )
         Print(" Field=",Size(ri!.field));
     fi;
     if not IsLeaf(ri) then
-        Print("\n",String("",level)," F:");
+        Print("\n",String("",level)," I:");
         if HasImageRecogNode(ri) then
             RECOG_ViewObj(level+3, ImageRecogNode(ri));
         else
@@ -81,6 +81,18 @@ InstallMethod( ViewObj, "for recognition nodes", [IsRecogNode],
     RECOG_ViewObj(0, ri);
   end);
 
+InstallMethod( NiceGens, "for a recognition node",
+[IsRecogNode],
+  function(ri)
+    return NiceGens(ri, GeneratorsOfGroup(Grp(ri)));
+  end );
+
+InstallOtherMethod( NiceGens, "for a recognition node and a list",
+[IsRecogNode, IsList],
+  function(ri,origgens)
+    return calcnicegens(ri)(ri,origgens);
+  end );
+
 
 #############################################################################
 # The main recursive function:
@@ -446,7 +458,6 @@ InstallGlobalFunction( RecogniseGeneric,
     else
         ri := EmptyRecognitionInfoRecord(knowledge,H,false);
     fi;
-    # was here earlier: Setcalcnicegens(ri,CalcNiceGensGeneric);
     Setmethodsforfactor(ri,methoddb);
 
     # Find a possible homomorphism (or recognise this group as leaf)
@@ -530,12 +541,12 @@ InstallGlobalFunction( RecogniseGeneric,
             return fail;
         fi;
 
-        Add(depthString,'F');
+        Add(depthString,'I');
         rifac := RecogniseGeneric(
                   Group(List(GeneratorsOfGroup(H), x->ImageElm(Homom(ri),x))),
-                  methodsforfactor(ri), depthString, forfactor(ri) ); # TODO: change forfactor to hintsForFactor??)
+                  methodsforfactor(ri), depthString, forfactor(ri) );
         Remove(depthString);
-        PrintTreePos("F",depthString,H);
+        PrintTreePos("I",depthString,H);
         SetImageRecogNode(ri,rifac);
         SetRIParent(rifac,ri);
 
@@ -555,7 +566,7 @@ InstallGlobalFunction( RecogniseGeneric,
 
         # Now we want to have preimages of the new generators in the image:
         Info(InfoRecog,2,"Calculating preimages of nice generators.");
-        ri!.pregensfacwithmem := CalcNiceGens(rifac, ri!.gensHmem);
+        ri!.pregensfacwithmem := NiceGens(rifac, ri!.gensHmem);
         Setpregensfac(ri, StripMemory(ri!.pregensfacwithmem));
 
         # Now create the kernel generators with the stored method:
@@ -654,14 +665,8 @@ InstallGlobalFunction( RecogniseGeneric,
         fi;
     until done;
 
-    if IsReady(riker) then    # we are only ready when the kernel is
-        # Now make the two projection slps:
-        SetNiceGens(ri,Concatenation(pregensfac(ri), NiceGens(riker)));
-        #ll := List([1..Length(NiceGens(rifac))],i->[i,1]);
-        #ri!.proj1 := StraightLineProgramNC([ll],Length(NiceGens(ri)));
-        #ll := List([1..Length(NiceGens(riker))],
-        #           i->[i+Length(NiceGens(rifac)),1]);
-        #ri!.proj2 := StraightLineProgramNC([ll],Length(NiceGens(ri)));
+    # we are only ready when the kernel is
+    if IsReady(riker) then
         SetFilterObj(ri,IsReady);
     fi;
     if InfoLevel(InfoRecog) = 1 and depth = 0 then Print("\n"); fi;
@@ -678,11 +683,6 @@ InstallGlobalFunction( ValidateHomomInput,
     fi;
   end );
 
-InstallGlobalFunction( CalcNiceGens,
-  function(ri,origgens)
-    return calcnicegens(ri)(ri,origgens);
-  end );
-
 InstallGlobalFunction( CalcNiceGensGeneric,
   # generic function using an slp:
   function(ri,origgens)
@@ -696,16 +696,32 @@ InstallGlobalFunction( CalcNiceGensGeneric,
 InstallGlobalFunction( CalcNiceGensHomNode,
   # function for the situation on a homomorphism node (non-Leaf):
   function(ri, origgens)
-    local nicegens, kernelgens;
+    local nicegens, nicekernelgens, x, kernelgens;
     # compute preimages of the nicegens of the image group
-    nicegens := CalcNiceGens(ImageRecogNode(ri), origgens);
+    nicegens := NiceGens(ImageRecogNode(ri), origgens);
     # Is there a non-trivial kernel? then add its nicegens
     if HasKernelRecogNode(ri) and KernelRecogNode(ri) <> fail then
         # we cannot just use gensN(KernelRecogNode(ri)) here, as those values are defined
         # relative to the original generators we used during recognition; but
         # the origgens passed to this function might differ
-        kernelgens := ResultOfStraightLineProgram(gensNslp(ri), origgens);
-        Append(nicegens, CalcNiceGens(KernelRecogNode(ri), kernelgens));
+        if origgens = GeneratorsOfGroup(Grp(ri)) then
+            # Print("HIT\n");
+            #Error("break");
+            nicekernelgens := NiceGens(KernelRecogNode(ri));
+            if IsObjWithMemory(origgens[1]) then
+                nicekernelgens := GeneratorsWithMemory(nicekernelgens);
+                # HACK!
+                for x in nicekernelgens do
+                    x!.slp := origgens[1]!.slp;
+                od;
+            fi;
+        else
+            # when recognizing, origgens have memory. When recognition is finished,
+            # these are usually without memory?
+            kernelgens := ResultOfStraightLineProgram(gensNslp(ri), origgens);
+            nicekernelgens := NiceGens(KernelRecogNode(ri), kernelgens);
+        fi;
+        Append(nicegens, nicekernelgens);
     fi;
     return nicegens;
   end );
@@ -858,7 +874,7 @@ InstallGlobalFunction( "SLPforNiceGens", function(ri)
   local l,ll,s;
   l := List( [1..Length(GeneratorsOfGroup(Grp(ri)))], x->() );
   l := GeneratorsWithMemory(l);
-  ll := CalcNiceGens(ri,l);
+  ll := NiceGens(ri,l);
   s := SLPOfElms(ll);
   if s <> fail then
       SlotUsagePattern(s);
@@ -955,7 +971,9 @@ RECOG.TestGroup := function(g,proj,size, optionlist...)
   if IsEmpty(gens) then
     gens := [One(g)];
   fi;
-  l := CalcNiceGens(ri,gens);
+  l := NiceGens(ri,gens);
+  l := NiceGens(ri,gens);
+  # Test whether SLPForNiceGens gives the same slps
   repeat
       count := count + 1;
       #Print(".\c");
diff --git a/gap/generic/KnownNilpotent.gi b/gap/generic/KnownNilpotent.gi
index a4525459f..88923560e 100644
--- a/gap/generic/KnownNilpotent.gi
+++ b/gap/generic/KnownNilpotent.gi
@@ -66,8 +66,8 @@ RECOG.CalcNiceGensKnownNilpotent := function(ri,origgens)
   local kernelgens;
   kernelgens := List([1..Length(ri!.decompositionExponents)],
                      i -> origgens[i]^ri!.decompositionExponents[i]);
-  return Concatenation(CalcNiceGens(ImageRecogNode(ri), origgens),
-                       CalcNiceGens(KernelRecogNode(ri), kernelgens));
+  return Concatenation(NiceGens(ImageRecogNode(ri), origgens),
+                       NiceGens(KernelRecogNode(ri), kernelgens));
 end;
 
 #! @BeginChunk KnownNilpotent
diff --git a/misc/colva/DPleaf.g b/misc/colva/DPleaf.g
index 8d00a8fe5..7ebe6f06e 100644
--- a/misc/colva/DPleaf.g
+++ b/misc/colva/DPleaf.g
@@ -320,7 +320,7 @@ SolveLeafDP := function(ri,rifac,name)
  blkdata := RecogniseLeaf(riH1,blk,name);;
 
 # Get the inverse images of the nice generators of blk in H1
- invims := CalcNiceGens(blkdata,GeneratorsOfGroup(H1));
+ invims := NiceGens(blkdata,GeneratorsOfGroup(H1));
  Yhat := ShallowCopy(invims);
  blktoH1 := GroupHomomorphismByFunction(blk,Grp(ri),g->
 ResultOfStraightLineProgram( SLPforElement(blkdata,g),invims));
diff --git a/misc/colva/Evaluate.g b/misc/colva/Evaluate.g
index 967275608..5eebdaf22 100644
--- a/misc/colva/Evaluate.g
+++ b/misc/colva/Evaluate.g
@@ -242,7 +242,7 @@ InstallGlobalFunction( NormalTree,
         # Now we want to have preimages of the new generators in the image:
       if not IsBound(ri!.pregensfac) then
         Info(InfoRecognition,1,"Calculating preimages of nice generators.");
-        Setpregensfac( ri, CalcNiceGens(rifac,GeneratorsOfGroup(H)));
+        Setpregensfac( ri, NiceGens(rifac,GeneratorsOfGroup(H)));
       fi;
         Setcalcnicegens(ri,CalcNiceGensHomNode);
 
diff --git a/misc/colva/README.md b/misc/colva/README.md
new file mode 100644
index 000000000..a694782a2
--- /dev/null
+++ b/misc/colva/README.md
@@ -0,0 +1,4 @@
+This is probably an attempt by Colva Roney-Dougal to port an implementation of
+Mark Stather (a PhD Student of Derek Holt) for computing sylow subgroups of
+matrix groups. That may have needed "normal trees" and chief series. The main
+file might be `NSM.g`?
diff --git a/tst/working/quick/bugfix.tst b/tst/working/quick/bugfix.tst
index bb03aa115..fcdc3f0b0 100644
--- a/tst/working/quick/bugfix.tst
+++ b/tst/working/quick/bugfix.tst
@@ -34,27 +34,27 @@ gap> old:=InfoLevel(InfoRecog);;
 gap> SetInfoLevel(InfoRecog, 0);
 gap> RecogniseGroup(SL(2,2));
 <recognition node GoProjective Dim=2 Field=2
- F:<recognition node (projective) ClassicalNatural_PSL2Even Size=6 Dim=
+ I:<recognition node (projective) ClassicalNatural_PSL2Even Size=6 Dim=
 2 Field=2>
  K:<trivial kernel>
 gap> RecogniseGroup(SL(2,3));
 <recognition node GoProjective Dim=2 Field=3
- F:<recognition node (projective) ClassicalNatural_PSL2Odd Size=12 Dim=
+ I:<recognition node (projective) ClassicalNatural_PSL2Odd Size=12 Dim=
 2 Field=3>
  K:<recognition node DiagonalMatrices Dim=2 Field=3
-    F:<recognition node Scalar Dim=1 Field=3>
+    I:<recognition node Scalar Dim=1 Field=3>
     K:<trivial kernel>>
 gap> RecogniseGroup(SL(2,4));
 <recognition node GoProjective Dim=2 Field=4
- F:<recognition node (projective) ClassicalNatural_PSL2Even Simple Size=
+ I:<recognition node (projective) ClassicalNatural_PSL2Even Simple Size=
 60 Dim=2 Field=4>
  K:<trivial kernel>
 gap> RecogniseGroup(SL(2,5));
 <recognition node GoProjective Dim=2 Field=5
- F:<recognition node (projective) ClassicalNatural_PSL2Odd Simple Size=60 Dim=
+ I:<recognition node (projective) ClassicalNatural_PSL2Odd Simple Size=60 Dim=
 2 Field=5>
  K:<recognition node DiagonalMatrices Dim=2 Field=5
-    F:<recognition node Scalar Dim=1 Field=5>
+    I:<recognition node Scalar Dim=1 Field=5>
     K:<trivial kernel>>
 gap> SetInfoLevel(InfoRecog, old);