Fix manual examples modified after PR #896

doc/ref/grpfp.xml

@@ -269,7 +269,7 @@ gap> f := FreeGroup( "a", "b" );
 gap> g := f / [ f.1^2, f.2^3, (f.1*f.2)^5 ];
 <fp group on the generators [ a, b ]>
 gap> h := IsomorphismPermGroup( g );
-[ a, b ] -> [ (1,2)(3,5), (2,3,4) ]
+[ a, b ] -> [ (1,2)(4,5), (2,3,4) ]
 gap> u:=Subgroup(g,[g.1*g.2]);;rt:=RightTransversal(g,u);
 RightTransversal(<fp group of size 60 on the generators 
 [ a, b ]>,Group([ a*b ]))

doc/tut/group.xml

@@ -832,9 +832,9 @@ usual way we now look for the subgroups above <C>u105</C>.
 gap> blocks := Blocks( a8, orb );; Length( blocks );
 15
 gap> blocks[1];
-[ (1,2)(3,4)(5,6)(7,8), (1,3)(2,4)(5,8)(6,7), (1,4)(2,3)(5,7)(6,8), 
-  (1,5)(2,6)(3,8)(4,7), (1,6)(2,5)(3,7)(4,8), (1,7)(2,8)(3,6)(4,5), 
-  (1,8)(2,7)(3,5)(4,6) ]
+[ (1,2)(3,4)(5,6)(7,8), (1,3)(2,4)(5,7)(6,8), (1,4)(2,3)(5,8)(6,7), 
+  (1,5)(2,6)(3,7)(4,8), (1,6)(2,5)(3,8)(4,7), (1,7)(2,8)(3,5)(4,6), 
+  (1,8)(2,7)(3,6)(4,5) ]
 ]]></Example>
 <P/>
 To find the subgroup of index 15 we  again use closure. Now  we must be a
@@ -1175,7 +1175,7 @@ gap> niceaut := NiceObject( aut );
 Group([ (1,4,2,3), (1,5,4)(2,6,3), (1,2)(3,4), (3,4)(5,6) ])
 gap> IsomorphismGroups( niceaut, SymmetricGroup( 4 ) );
 [ (1,4,2,3), (1,5,4)(2,6,3), (1,2)(3,4), (3,4)(5,6) ] -> 
-[ (1,4,3,2), (1,4,2), (1,3)(2,4), (1,4)(2,3) ]
+[ (1,2,4,3), (2,4,3), (1,4)(2,3), (1,2)(3,4) ]
 ]]></Example>
 <P/>
 The range of  a nice monomorphism is  in most cases a permutation  group,

lib/ctbl.gd

@@ -4373,18 +4373,18 @@ DeclareGlobalFunction( "NormalSubgroupClasses" );
 ##    Character( CharacterTable( S4 ), [ 3, 1, -1, 0, -1 ] ), 
 ##    Character( CharacterTable( S4 ), [ 1, 1, 1, 1, 1 ] ) ]
 ##  gap> kernel:= KernelOfCharacter( irr[3] );
-##  Group([ (1,2)(3,4), (1,3)(2,4) ])
+##  Group([ (1,2)(3,4), (1,4)(2,3) ])
 ##  gap> HasNormalSubgroupClassesInfo( tbl );
 ##  true
 ##  gap> NormalSubgroupClassesInfo( tbl );
-##  rec( nsg := [ Group([ (1,2)(3,4), (1,3)(2,4) ]) ],
+##  rec( nsg := [ Group([ (1,2)(3,4), (1,4)(2,3) ]) ], 
 ##    nsgclasses := [ [ 1, 3 ] ], nsgfactors := [  ] )
 ##  gap> ClassPositionsOfNormalSubgroup( tbl, kernel );
 ##  [ 1, 3 ]
 ##  gap> FactorGroupNormalSubgroupClasses( tbl, [ 1, 3 ] );
 ##  Group([ f1, f2 ])
 ##  gap> NormalSubgroupClassesInfo( tbl );
-##  rec( nsg := [ Group([ (1,2)(3,4), (1,3)(2,4) ]) ],
+##  rec( nsg := [ Group([ (1,2)(3,4), (1,4)(2,3) ]) ], 
 ##    nsgclasses := [ [ 1, 3 ] ], nsgfactors := [ Group([ f1, f2 ]) ] )
 ##  ]]></Example>
 ##  </Description>

lib/grp.gd

@@ -3248,7 +3248,7 @@ KeyDependentOperation( "PCore", IsGroup, IsPosInt, "prime" );
 ##  <M>V \geq </M><A>U</A>. If <A>U</A> is subnormal, <M>V =</M> <A>U</A>.
 ##  <Example><![CDATA[
 ##  gap> s:=SubnormalSeries(g,Group((1,2)(3,4)));
-##  [ Group([ (1,2,3,4), (1,2) ]), Group([ (1,2)(3,4), (1,4)(2,3) ]), 
+##  [ Group([ (1,2,3,4), (1,2) ]), Group([ (1,2)(3,4), (1,3)(2,4) ]), 
 ##    Group([ (1,2)(3,4) ]) ]
 ##  ]]></Example>
 ##  </Description>
@@ -4151,12 +4151,14 @@ DeclareAttribute( "IsomorphismFpGroup", IsGroup );
 ##  <Example><![CDATA[
 ##  gap> SetInfoLevel( InfoFpGroup, 1 );
 ##  gap> iso := IsomorphismFpGroupByGenerators( g, [ (1,2), (1,2,3,4,5) ] );
-##  #I  the image group has 2 gens and 5 rels of total length 39
+##  #I  the image group has 2 gens and 4 rels of total length 50
 ##  [ (1,2), (1,2,3,4,5) ] -> [ F1, F2 ]
 ##  gap> fp := Image( iso );
 ##  <fp group of size 120 on the generators [ F1, F2 ]>
 ##  gap> RelatorsOfFpGroup( fp );
-##  [ F1^2, F2^5, (F2^-1*F1)^4, (F1*F2^-1*F1*F2)^3, (F1*F2^2*F1*F2^-2)^2 ]
+##  [ F1^2, (F2*F1*F2^-2*F1)^3, 
+##    F2*F1*F2^-1*(F1*F2)^2*F2^2*(F1*F2^-1)^2*F2^-1*F1, 
+##    (F2*F1*F2^-1*F1)^2*F2^-1*F1*F2^2*F1*F2^-2*F1*F2*F1 ]
 ##  ]]></Example>
 ##  <P/>
 ##  The main task of the function
@@ -4183,9 +4185,9 @@ DeclareAttribute( "IsomorphismFpGroup", IsGroup );
 ##    (1,12)(2,11)(3,6)(4,8)(5,9)(7,10) ])
 ##  gap> gens := GeneratorsOfGroup( M12 );;
 ##  gap> iso := IsomorphismFpGroupByGenerators( M12, gens );;
-##  #I  the image group has 3 gens and 20 rels of total length 464
+##  #I  the image group has 3 gens and 21 rels of total length 459
 ##  gap> iso := IsomorphismFpGroupByGenerators( M12, gens );;
-##  #I  the image group has 3 gens and 19 rels of total length 491
+##  #I  the image group has 3 gens and 18 rels of total length 337
 ##  ]]></Example>
 ##  <P/>
 ##  Also in the case of a permutation group <A>G</A>, the function
@@ -4234,7 +4236,7 @@ DeclareAttribute( "IsomorphismFpGroup", IsGroup );
 ##  #I  the image group has 3 gens and 11 rels of total length 92
 ##  gap> iso := IsomorphismFpGroupByGenerators( M12, gens : 
 ##  >                                           method := "fast" );;
-##  #I  the image group has 3 gens and 179 rels of total length 4099
+##  #I  the image group has 3 gens and 153 rels of total length 3374
 ##  ]]></Example>
 ##  <P/>
 ##  Though the option <C>method := "regular"</C> is only checked in the case
@@ -4256,7 +4258,7 @@ DeclareAttribute( "IsomorphismFpGroup", IsGroup );
 ##    [ [ 0, 1, 0, 0, 0 ], [ 0, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0 ], 
 ##        [ 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1 ] ] ]
 ##  gap> iso := IsomorphismFpGroupByGenerators( G, gens );;
-##  #I  the image group has 2 gens and 9 rels of total length 94
+##  #I  the image group has 2 gens and 10 rels of total length 122
 ##  gap> iso := IsomorphismFpGroupByGenerators( G, gens : 
 ##  >                                           method := "regular");;
 ##  #I  the image group has 2 gens and 6 rels of total length 56
@@ -4268,15 +4270,7 @@ DeclareAttribute( "IsomorphismFpGroup", IsGroup );
 ##  , 0, 0, 0, 1 ] ] ]->[ F1, F2 ]>
 ##  gap> ConstituentsCompositionMapping(iso);
 ##  [ <action isomorphism>, 
-##  [ (2,3,5,9,16,29)(4,7,13,24,19,32)(6,11,20,34,40,57)(8,15,28,46,42,
-##      59)(10,18,25,41,49,67)(12,22,37,53,48,66)(14,26,31)(17,30,35,
-##      50,58,38)(21,36,33)(23,39,56)(27,44,61,72,43,60)(45,62,51,68,
-##      54,70)(47,64,73)(52,69)(55,71,75,78,77,76)(65,74), 
-##    (1,2,4,8)(3,6,12,23)(5,10,19,33)(7,14,27,45)(9,17,18,31)(11,21,
-##      16,28)(13,25,42,57)(20,35,51,67)(22,38,55,70)(24,40,26,43)(29,
-##      37,54,39)(30,47,65,68)(32,48)(34,49,36,52)(41,58,56,61)(44,50,
-##      53,64)(46,63,69,59)(60,66,75,79)(62,73,72,77)(71,76,80,74) 
-##   ] -> [ F1, F2 ] ]
+##    [ (2,3,4)(5,6)(8,9,10), (1,2,3,5)(6,7,8,9) ] -> [ F1, F2 ] ]
 ##  ]]></Example>
 ##  <P/>
 ##  Since &GAP; cannot decompose elements of a matrix group into generators,