Merge pull request #78 from rlutowsk/rl-leftcosets

correcting behaviour of `LeftCoset` creation

Author: cdwensley

doc/groups.xml

@@ -172,7 +172,7 @@ by converting <M>gU</M> to <M>Ug^{-1}</M>;
 applying the equivalent method for right cosets; 
 and, if necessary, converting back again to left cosets. 
 <P/> 
-<M>G</M> acts on <M>gU</M> by <C>OnLeftInverse</C>: 
+<M>G</M> acts on left cosets by <C>OnLeftInverse</C>:
 <M>(gU)^{g_0} = g_0^{-1}*(gU) = (g_0^{-1}g)U</M>. 
 <P/>
 </Description>

lib/lcset.gi

@@ -23,7 +23,7 @@ function( g, U )
     ObjectifyWithAttributes( lc, fam!.leftCosetsDefaultType,
         Representative, g,
         ActingDomain, U, 
-        FunctionAction, OnLeftInverse, 
+        FunctionAction, OnRight,
         IsLeftCoset, true ); 
     if HasSize( U ) then 
         SetSize( lc, Size( U ) ); 

tst/lcset.tst

@@ -26,6 +26,10 @@ gap> IsBiCoset( LeftCoset( (1,7), AlternatingGroup(6) ) );
 false
 gap> IsLeftCoset( LeftCoset( (1,2,3), MathieuGroup(12) ) );
 true
+gap> g:=SymmetricGroup(3);;
+gap> h:=Group((1,2));;
+gap> List(LeftCosets(g,h), SSortedList);
+[ [ (), (1,2) ], [ (1,3,2), (1,3) ], [ (2,3), (1,2,3) ] ]
 
 # test intersecting permutation cosets 
 gap> H1 := Group( [ (), (2,7,6)(3,4,5), (1,2,7,5,6,4,3) ] );;