Fix one IsPNilpotent method, and add some tests

lib/grp.gi

@@ -2622,7 +2622,7 @@ InstallMethod( IsPNilpotentOp,
     local primes, S;
 
     primes:= PrimeDivisors( Size( G ) );
-    RemoveSet( primes, p );
+    primes:= Filtered(primes, q -> q <> p );
     S:= HallSubgroup( G, primes );
 
     return S <> fail and IsNormal( G, S );

tst/testinstall/opers/IsPNilpotent.tst

@@ -0,0 +1,15 @@
+gap> START_TEST("IsPNilpotent.tst");
+
+#
+gap> G:=SymmetricGroup(3);;
+gap> List([2,3,5], p -> IsPNilpotent(G,p));
+[ true, false, true ]
+
+#
+gap> G:=SymmetricGroup(3);;
+gap> SpecialPcgs(G);;
+gap> List([2,3,5], p -> IsPNilpotent(G,p));
+[ true, false, true ]
+
+#
+gap> STOP_TEST("IsPNilpotent.tst", 10000);

tst/testinstall/opers/SimpleGroup.tst

@@ -0,0 +1,28 @@
+gap> START_TEST("SimpleGroup.tst");
+
+#
+gap> SimpleGroup("Sz(8)");
+Sz(8)
+gap> SimpleGroup("Suzuki(32)");
+Sz(32)
+gap> SimpleGroup("Suz(8)");
+Sz(8)
+gap> SimpleGroup("Sz(9)");
+Error, Illegal Parameter for Suzuki groups
+gap> SimpleGroup("Suz(16)");
+Error, Illegal Parameter for Suzuki groups
+
+#
+gap> SimpleGroup("R(27)");
+Ree(27)
+gap> SimpleGroup("Ree(27)");
+Ree(27)
+gap> SimpleGroup("2G(243)");
+Ree(243)
+gap> SimpleGroup("Ree(9)");
+Error, Illegal Parameter for Ree groups
+gap> SimpleGroup("Ree(16)");
+Error, Illegal Parameter for Ree groups
+
+#
+gap> STOP_TEST("SimpleGroup.tst", 10000);

tst/testinstall/opers/SubdirectProducts.tst

@@ -0,0 +1,33 @@
+gap> START_TEST("SubdirectProducts.tst");
+gap> G := SymmetricGroup(3);;
+gap> H := SymmetricGroup(4);;
+gap> A := CyclicGroup(6);;
+
+#
+gap> Set(SubdirectProducts(G, G), IdGroup);
+[ [ 6, 1 ], [ 18, 4 ], [ 36, 10 ] ]
+gap> Set(SubdirectProducts(H, H), IdGroup);
+[ [ 24, 12 ], [ 96, 227 ], [ 288, 1026 ], [ 576, 8653 ] ]
+gap> Set(SubdirectProducts(A, A), IdGroup);
+[ [ 6, 2 ], [ 12, 5 ], [ 18, 5 ], [ 36, 14 ] ]
+
+#
+gap> Set(SubdirectProducts(G, H), IdGroup);
+[ [ 24, 12 ], [ 72, 43 ], [ 144, 183 ] ]
+gap> Set(SubdirectProducts(H, G), IdGroup);
+[ [ 24, 12 ], [ 72, 43 ], [ 144, 183 ] ]
+
+#
+gap> Set(SubdirectProducts(G, A), IdGroup);
+[ [ 18, 3 ], [ 36, 12 ] ]
+gap> Set(SubdirectProducts(A, G), IdGroup);
+[ [ 18, 3 ], [ 36, 12 ] ]
+
+#
+gap> Set(SubdirectProducts(H, A), IdGroup);
+[ [ 72, 42 ], [ 144, 188 ] ]
+gap> Set(SubdirectProducts(A, H), IdGroup);
+[ [ 72, 42 ], [ 144, 188 ] ]
+
+#
+gap> STOP_TEST("SubdirectProducts.tst", 10000);