Turn IsInfiniteAbelianizationGroup into a property

Also add some true methods (e.g. finite groups never have
infinite abelianization; all but trivial free groups do have
infinite abelianization), and some tests

lib/grp.gd

@@ -857,7 +857,12 @@ DeclareAttribute( "AbelianInvariants", IsGroup );
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
-DeclareAttribute( "IsInfiniteAbelianizationGroup", IsGroup );
+DeclareProperty( "IsInfiniteAbelianizationGroup", IsGroup );
+
+# finite groups never have infinite abelianization
+InstallTrueMethod( HasIsInfiniteAbelianizationGroup, IsGroup and IsFinite );
+
+#InstallTrueMethod( IsInfiniteAbelianizationGroup, IsSolvableGroup and IsTorsionFree );
 
 
 #############################################################################

lib/grpfp.gi

@@ -907,6 +907,10 @@ function(H)
 
 end);
 
+# a free group has infinite abelianization if and only if it is non-trivial
+InstallTrueMethod( IsInfiniteAbelianizationGroup, IsFreeGroup and IsNonTrivial );
+InstallTrueMethod( HasIsInfiniteAbelianizationGroup, IsFreeGroup and IsTrivial );
+
 #############################################################################
 ##
 #M  IsPerfectGroup( <H> )

tst/testinstall/opers/IsInfiniteAbelianizationGroup.g

@@ -0,0 +1,49 @@
+gap> START_TEST("IsInfiniteAbelianizationGroup.tst");
+
+#
+# Finite groups never have infinite abelianization
+#
+gap> G:=SymmetricGroup(3);;
+gap> HasIsInfiniteAbelianizationGroup(G);
+true
+gap> IsInfiniteAbelianizationGroup(G);
+false
+
+#
+# Free groups have infinite abelianization if and only if they are non-trivial
+#
+gap> G:=FreeGroup(0);;
+gap> HasIsInfiniteAbelianizationGroup(G);
+true
+gap> IsInfiniteAbelianizationGroup(G);
+false
+
+#
+gap> G:=FreeGroup(2);;
+gap> HasIsInfiniteAbelianizationGroup(G);
+true
+gap> IsInfiniteAbelianizationGroup(G);
+true
+
+#
+gap> G:=TrivialSubgroup(G);;
+gap> HasIsInfiniteAbelianizationGroup(G);
+true
+gap> IsInfiniteAbelianizationGroup(G);
+false
+
+#
+# for fp groups, more work is needed
+#
+gap> F:=FreeGroup(2);;
+gap> H:=F/[F.1^2,F.2^2];; IsInfiniteAbelianizationGroup(H);
+false
+gap> H:=F/[F.1^2];; IsInfiniteAbelianizationGroup(H);
+true
+gap> H:=F/[F.1^2,F.2^2,Comm(F.1,F.2)];; IsInfiniteAbelianizationGroup(H);
+false
+gap> K:=Subgroup(H, [H.1, H.2^2]);; IsInfiniteAbelianizationGroup(K);
+false
+
+#
+gap> STOP_TEST("IsInfiniteAbelianizationGroup.tst", 1);