Turn IsInfiniteAbelianizationGroup into a property

Also add some implications for it, e.g. finite groups never have infinite abelianization; all but trivial free groups do have infinite abelianization). Finally, add some tests.
gap-system · Mar 23, 2018 · ecb00ad · ecb00ad
1 parent 9da60a3
commit ecb00ad
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Showing 5 changed files with 67 additions and 7 deletions.
diff --git a/hpcgap/lib/object.gd b/hpcgap/lib/object.gd
@@ -740,7 +740,8 @@ DeclareOperation( "KnownPropertiesOfObject", [ IsObject ] );
 ##    "IsCompletelyRegularSemigroup", "IsCompletelySimpleSemigroup", 
 ##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup", 
 ##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup", 
-##    "KnowsHowToDecompose", "IsNilpotentByFinite" ]
+##    "KnowsHowToDecompose", "IsInfiniteAbelianizationGroup", 
+##    "IsNilpotentByFinite" ]
 ##  gap> Size(g);
 ##  6
 ##  gap> KnownPropertiesOfObject(g);
@@ -753,8 +754,8 @@ DeclareOperation( "KnownPropertiesOfObject", [ IsObject ] );
 ##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup", 
 ##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup", 
 ##    "KnowsHowToDecompose", "IsPerfectGroup", "IsSolvableGroup", 
-##    "IsPolycyclicGroup", "IsNilpotentByFinite", "IsTorsionFree", 
-##    "IsFreeAbelian" ]
+##    "IsPolycyclicGroup", "IsInfiniteAbelianizationGroup", 
+##    "IsNilpotentByFinite", "IsTorsionFree", "IsFreeAbelian" ]
 ##  gap> KnownTruePropertiesOfObject(g);
 ##  [ "IsNonTrivial", "IsFinite", "CanEasilyCompareElements", 
 ##    "CanEasilySortElements", "IsDuplicateFree", 

diff --git a/lib/grp.gd b/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 );
 
 
 #############################################################################

diff --git a/lib/grpfp.gi b/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> )

diff --git a/lib/object.gd b/lib/object.gd
@@ -714,7 +714,8 @@ DeclareOperation( "KnownPropertiesOfObject", [ IsObject ] );
 ##    "IsCompletelyRegularSemigroup", "IsCompletelySimpleSemigroup", 
 ##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup", 
 ##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup", 
-##    "KnowsHowToDecompose", "IsNilpotentByFinite" ]
+##    "KnowsHowToDecompose", "IsInfiniteAbelianizationGroup", 
+##    "IsNilpotentByFinite" ]
 ##  gap> Size(g);
 ##  6
 ##  gap> KnownPropertiesOfObject(g);
@@ -727,8 +728,8 @@ DeclareOperation( "KnownPropertiesOfObject", [ IsObject ] );
 ##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup", 
 ##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup", 
 ##    "KnowsHowToDecompose", "IsPerfectGroup", "IsSolvableGroup", 
-##    "IsPolycyclicGroup", "IsNilpotentByFinite", "IsTorsionFree", 
-##    "IsFreeAbelian" ]
+##    "IsPolycyclicGroup", "IsInfiniteAbelianizationGroup", 
+##    "IsNilpotentByFinite", "IsTorsionFree", "IsFreeAbelian" ]
 ##  gap> KnownTruePropertiesOfObject(g);
 ##  [ "IsNonTrivial", "IsFinite", "CanEasilyCompareElements", 
 ##    "CanEasilySortElements", "IsDuplicateFree", 

diff --git a/tst/testinstall/opers/IsInfiniteAbelianizationGroup.g b/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);