ENHANCE: Isomorphism test can deal with fp groups etc.

Close gap-system#963

lib/autsr.gi

@@ -787,7 +787,7 @@ end);
 # pathetic isomorphism test, based on the automorphism group of GxH. This is
 # only of use as long as we don't yet have a Cannon/Holt version of
 # isomorphism available and there are many generators
-BindGlobal("PatheticIsomorphism",function(G,H)
+InstallGlobalFunction(PatheticIsomorphism,function(G,H)
 local d,a,map,possibly,cG,cH,nG,nH,i,j,sel,u,v,asAutomorphism,K,L,conj,e1,e2,
       iso,api,good,gens,pre;
   possibly:=function(a,b)
@@ -807,6 +807,28 @@ local d,a,map,possibly,cG,cH,nG,nH,i,j,sel,u,v,asAutomorphism,K,L,conj,e1,e2,
     return Image(hom,sub);
   end;
 
+  # TODO: use matgrp package
+  if not (IsPermGroup(G) or IsPcGroup(G))  then
+    i:=IsomorphismPermGroup(G);
+    iso:=PatheticIsomorphism(Image(i,G),H);
+    if iso=fail then
+      return iso;
+    else
+      return i*iso;
+    fi;
+  fi;
+
+  # TODO: use matgrp package
+  if not (IsPermGroup(H) or IsPcGroup(H)) then
+    i:=IsomorphismPermGroup(H);
+    iso:=PatheticIsomorphism(G,Image(i,H));
+    if iso=fail then
+      return iso;
+    else
+      return iso*InverseGeneralMapping(i);
+    fi;
+  fi;
+
   # go through factors of characteristic series to keep orbits short.
   AutomorphismGroup(G:someCharacteristics:=fail);
   AutomorphismGroup(H:someCharacteristics:=fail);

lib/morpheus.gd

@@ -560,6 +560,7 @@ DeclareOperation("GQuotients",[IsGroup,IsGroup]);
 ##
 DeclareOperation("IsomorphicSubgroups",[IsGroup,IsGroup]);
 
+DeclareGlobalFunction("PatheticIsomorphism");
 
 #############################################################################
 ##

lib/morpheus.gi

@@ -2011,6 +2011,15 @@ InstallMethod( InnerAutomorphismsAutomorphismGroup,
 InstallGlobalFunction(IsomorphismGroups,function(G,H)
 local m;
 
+  if not HasIsFinite(G) or not HasIsFinite(H) then
+    Info(InfoWarning,1,"Forcing finiteness test");
+    IsFinite(G);
+    IsFinite(H);
+  fi;
+  if not IsFinite(G) and IsFinite(H) then
+    Error("cannot test isomorphism of infinite groups");
+  fi;
+
   #AH: Spezielle Methoden ?
   if Size(G)=1 then
     if Size(H)<>1 then