feat: Add IsLeftFPFInducted property

lib/properties.gd

@@ -291,3 +291,25 @@ DeclareProperty( "IsRightCancellative", IsMagma );
 #! @EndExampleSession
 #!
 DeclareProperty( "IsCancellative", IsMagma );
+
+#! @Arguments M
+#! @Description
+#! is a left-hand sided fixed-point free inducted <A>m</A>.
+#!
+#! @BeginExampleSession
+#! @EndExampleSession
+#!
+DeclareProperty( "IsLeftFPFInducted", IsMagma );
+
+#! @Arguments M
+#! @Description
+#! is a left-hand sided fixed-point free inducted <A>m</A>.
+#!
+#! @BeginExampleSession
+#! gap> List(AllSmallAntimagmas(2), M -> IsLeftFPFInducted(M) );
+#! [ false, true ]
+#! gap> List(AllSmallAntimagmas(2), M -> IsRightFPFInducted(M) );
+#! [ true, false ]
+#! @EndExampleSession
+#!
+DeclareProperty( "IsRightFPFInducted", IsMagma );

lib/properties.gi

@@ -230,4 +230,14 @@ end);
 InstallMethod(IsCancellative, "for a magma", [IsMagma],
     function(M)
         return IsLeftCancellative(M) and IsRightCancellative(M);
+end);
+
+InstallMethod(IsLeftFPFInducted, "for a magma", [IsMagma],
+    function(M)
+        return ForAll(M, m -> Size( Unique( m * Elements(M) ) ) = 1 and First( Unique( m * Elements(M) ) ) <> m);
+end);
+
+InstallMethod(IsRightFPFInducted, "for a magma", [IsMagma],
+    function(M)
+        return ForAll(M, m -> Size( Unique( Elements(M) * m ) ) = 1 and First( Unique( Elements(M) * m ) ) <> m);
 end);

tst/test_properties_magma_isfpf.tst

@@ -0,0 +1,19 @@
+gap> START_TEST( "test_properties_magma_isfpf.tst" );
+
+gap> M := MagmaByMultiplicationTable([ [1, 1], [2, 2] ] );;
+gap> IsLeftFPFInducted(MagmaByMultiplicationTable([ [1, 1], [2, 2] ] ));
+false
+gap> IsRightFPFInducted(MagmaByMultiplicationTable([ [1, 1], [2, 2] ] ));
+false
+
+gap> M := SmallAntimagma(2, 1);      
+<magma with 2 generators>
+gap> IsLeftFPFInducted( M );
+false
+gap> IsRightFPFInducted( M );
+true
+
+gap> Filtered( Filtered(AllSmallAntimagmas([2 .. 3]), M -> IsLeftFPFInducted(M)), M -> IsRightFPFInducted(M) );
+[  ]
+
+gap> STOP_TEST( "test_properties_magma_isfpf.tst" );