addressed some comments

doc/ref/grphomom.xml

@@ -346,6 +346,9 @@ faithful action of <C>G</C> on a small set of vectors.
 In such a case, one can prescribe this monomorphism via
 <C>SetNiceMonomorphism( G, map )</C>,
 provided that <C>map</C> stores that it is injective.
+The latter can be achieved by calling <C>IsInjective( map )</C> or,
+if one is sure that <C>map</C> is injective and one wants to avoid the
+overhead of the test, by calling <C>SetIsInjective( map, true )</C>.
 
 <#Include Label="IsHandledByNiceMonomorphism">
 <#Include Label="NiceMonomorphism">

doc/tut/group.xml

@@ -1216,6 +1216,11 @@ only if this map knows that it is injective.
 In the above example, this is the case because the map is created as the
 composition of two maps (a nice monomorphism and an isomorphism)
 which know that they are injective.
+In general, the injectivity flag of a map <C>map</C> gets set if one tests
+the property by calling <C>IsInjective( map )</C>;
+if one is sure that <C>map</C> is injective and wants to avoid the
+potentially expensive test then one can set the flag by explicitly
+calling <C>SetIsInjective( map, true )</C>.
 <P/>
 <E>Summary.</E>  In this section we have  seen  how calculations in groups
 can be carried  out in isomorphic  images in  nicer groups. We  have seen

lib/grpnice.gi

@@ -18,11 +18,8 @@
 ##
 ##  We install a special setter method because we have to make sure that only
 ##  injective maps get stored as nice monomorphisms.
-##  More precisely, we the stored map must know that it is injective,
+##  More precisely, the stored map must know that it is injective,
 ##  otherwise computing its kernel may run into an infinite recursion.
-##  (The maps computed by 'NiceMonomorphism' have the 'IsInjective' flag,
-##  the test affects only those maps that shall be set by hand as
-##  nice monomorphisms.)
 ##
 ##  Besides this, we want to tell every nice monomorphism that it is one.
 ##
@@ -114,8 +111,8 @@ InstallMethod( GroupByNiceMonomorphism,
 function( nice, grp )
     local   fam,  pre;
 
-    if not IsInjective( nice ) then
-      Error( "<nice> is not injective" );
+    if not ( HasIsInjective( nice ) and IsInjective( nice ) ) then
+      Error( "<nice> is not known to be injective" );
     fi;
     fam := FamilyObj( Source(nice) );
     pre := Objectify(NewType(fam,IsGroup and IsAttributeStoringRep), rec());