Fix IsNormal, uprank FittingSubgroup method(#61)

Our IsNormal method was buggy (it incorrectly used `Pcp(H,U)`. After fixing this it is mostly equivalent to GAP's default method; so we remove ours and use the default.

This in turn revealed that our `FittingSubgroup` method may not be invoked for finite pcp groups, depending on which packages are loaded. Fix that by increasing its rank.

gap/basic/pcpgrps.gi

@@ -158,22 +158,6 @@ function( H, U )
     return ForAll( GeneratorsOfGroup(U), x -> x in H );
 end );
 
-#############################################################################
-##
-#M IsNormal( H, U ) . . . . . . . . . . . . . . .test if U is normalized by H
-##
-InstallMethod( IsNormalOp, "for pcp groups",
-               IsIdenticalObj, [ IsPcpGroup, IsPcpGroup ],
-function( H, U )
-    local u, h;
-    for h in GeneratorsOfPcp( Pcp(H, U)) do
-        for u in Igs(U) do
-            if not u^h in U then return false; fi;
-        od;
-    od;
-    return true;
-end );
-
 #############################################################################
 ##
 #M Size( <pcpgrp> )

gap/pcpgrp/fitting.gi

@@ -56,6 +56,7 @@ end );
 ##
 InstallMethod( FittingSubgroup,
                "for pcp groups", [IsPcpGroup],
+			   SUM_FLAGS, # Prevent generic GAP library method for finite groups being ranked higher
 function( G )
     local efas, pcps, l, F, i;
 
@@ -253,4 +254,3 @@ InstallGlobalFunction( NilpotentByAbelianByFiniteSeries, function( G )
     if IndexNC( G, A ) = infinity then Error("wrong subgroup"); fi;
     return [G, A, F, U];
 end );
-

tst/bugfix.tst

@@ -497,5 +497,20 @@ true
 gap> Random( TrivialGroup( IsPcpGroup ) );
 id
 
+#
+# Fix a bug in IsNormal
+# <https://github.com/gap-packages/polycyclic/issues/46>
+#
+gap> g := PcGroupToPcpGroup(SmallGroup(48,1));
+Pcp-group with orders [ 2, 2, 2, 2, 3 ]
+gap> S := SylowSubgroup( g, 2 );
+Pcp-group with orders [ 2, 2, 2, 2 ]
+gap> T := S^g.5;
+Pcp-group with orders [ 2, 2, 2, 2 ]
+gap> IsNormal( S, T );
+false
+gap> IsNormal( T, S );
+false
+
 #
 gap> STOP_TEST( "bugfix.tst", 10000000);