diff --git a/lib/fieldfin.gi b/lib/fieldfin.gi
index bcae34fc13..512f730fe4 100644
--- a/lib/fieldfin.gi
+++ b/lib/fieldfin.gi
@@ -79,7 +79,14 @@ InstallMethodWithRandomSource( Random,
 InstallMethod( Units,
     "for a finite field",
     [ IsField and IsFinite ],
-    F -> GroupByGenerators( [ PrimitiveRoot( F ) ] ) );
+    function ( F )
+    local G;
+    G := GroupByGenerators( [ PrimitiveRoot( F ) ] );
+    if HasSize( F ) then
+      SetSize( G, Size( F )-1 );
+    fi;
+    return G;
+    end );
 
 
 #############################################################################
diff --git a/lib/grp.gd b/lib/grp.gd
index 5134ca73e7..35b00f6173 100644
--- a/lib/grp.gd
+++ b/lib/grp.gd
@@ -253,9 +253,10 @@ InstallSubsetMaintenance( IsSubsetLocallyFiniteGroup,
 
 #############################################################################
 ##
-#M  IsSubsetLocallyFiniteGroup( <G> ) . . . . . . . . . .  for magmas of FFEs
+#M  IsSubsetLocallyFiniteGroup( <G> ) . . .  for magmas with inverses of FFEs
 ##
-InstallTrueMethod( IsSubsetLocallyFiniteGroup, IsFFECollection and IsMagma );
+InstallTrueMethod( IsSubsetLocallyFiniteGroup,
+    IsFFECollection and IsMagmaWithInverses );
 
 
 #############################################################################
diff --git a/lib/grpffmat.gd b/lib/grpffmat.gd
index 76162043dd..518b5faed4 100644
--- a/lib/grpffmat.gd
+++ b/lib/grpffmat.gd
@@ -30,13 +30,15 @@ DeclareSynonym( "IsFFEMatrixGroup", IsFFECollCollColl and IsMatrixGroup );
 
 #############################################################################
 ##
-#M  IsFinite( <ffe-mat-grp> )
+#M  IsSubsetLocallyFiniteGroup( <ffe-mat-grp> )
+##
+##  As a consequence, any IsFFEMatrixGroup in IsFinitelyGeneratedGroup
+##  automatically is also in IsFinite.
 ##
 ##  *Note:*  The following implication only holds  if  there are no  infinite
 ##  dimensional matrices.
 ##
-InstallTrueMethod( IsFinite,
-    IsFFEMatrixGroup and IsFinitelyGeneratedGroup );
+InstallTrueMethod( IsSubsetLocallyFiniteGroup, IsFFEMatrixGroup );
 
 
 #############################################################################
diff --git a/lib/ring.gd b/lib/ring.gd
index 31fd27bd1a..530d790c54 100644
--- a/lib/ring.gd
+++ b/lib/ring.gd
@@ -748,7 +748,7 @@ InstallFactorMaintenance( IsZeroMultiplicationRing,
 ##  gap> Units( GaussianIntegers );
 ##  [ -1, 1, -E(4), E(4) ]
 ##  gap> Units( GF( 16 ) );
-##  <group with 1 generators>
+##  <group of size 15 with 1 generators>
 ##  ]]></Example>
 ##  </Description>
 ##  </ManSection>
diff --git a/tst/testbugfix/2018-02-28-IsSubsetLocallyFiniteGroup.tst b/tst/testbugfix/2018-02-28-IsSubsetLocallyFiniteGroup.tst
new file mode 100644
index 0000000000..0527d2a1c1
--- /dev/null
+++ b/tst/testbugfix/2018-02-28-IsSubsetLocallyFiniteGroup.tst
@@ -0,0 +1,29 @@
+# there used to be a bad implication from IsFFECollection and IsMagma to
+# IsSubsetLocallyFiniteGroup, which caused all finite fields to be in filter
+# IsSubsetLocallyFiniteGroup -- verify this is not the case anymore.
+gap> HasIsSubsetLocallyFiniteGroup(GF(2));
+false
+gap> HasIsSubsetLocallyFiniteGroup(GF(2^20));
+false
+
+# that implication was replaced by one from IsFFECollection and IsMagmaWithInverses
+# to IsSubsetLocallyFiniteGroup -- verify that it works
+gap> G:=Units(GF(2));;
+gap> HasIsSubsetLocallyFiniteGroup(G);
+true
+gap> HasIsFinite(G);
+true
+
+#
+gap> G:=Group(Z(2));;
+gap> HasIsSubsetLocallyFiniteGroup(G);
+true
+gap> HasIsFinite(G);
+true
+
+#
+gap> G:=Group(Z(2^20));;
+gap> HasIsSubsetLocallyFiniteGroup(G);
+true
+gap> HasIsFinite(G);
+true