diff --git a/doc/intro.xml b/doc/intro.xml
index f6df25d..91e6444 100644
--- a/doc/intro.xml
+++ b/doc/intro.xml
@@ -30,11 +30,10 @@ how to use the main high-level functions provided by &LINS;.
We compute all normal subgroups in D_{50},
the dihedral group of size 50.
n := 50;;
-gap> G := DihedralGroup(n);
+gap> G := DihedralGroup(50);
gap> L := LowIndexNormalSubs(G, n);;
-gap> IsoTypes := List(L, H -> StructureDescription(H));
+gap> IsoTypes := List(L, StructureDescription);
[ "D50", "C25", "C5", "1" ]
]]>
@@ -46,13 +45,10 @@ gap> IsoTypes := List(L, H -> StructureDescription(H));
We compute all normal subgroups of index 5^2 = 25 in C_5^4,
the direct product of 4 copies of the cyclic group of order 5:
p := 5;;
-gap> d := 4;;
-gap> C := CyclicGroup(5);;
-gap> G := DirectProduct(ListWithIdenticalEntries(d, C));
+gap> G := ElementaryAbelianGroup(5^4);
gap> L := LowIndexNormalSubs(G, 5 ^ 2 : allSubgroups := false);;
-gap> IsoTypes := Collected(List(L, H -> StructureDescription(H)));
+gap> IsoTypes := Collected(List(L, StructureDescription));
[ [ "C5 x C5", 806 ] ]
]]>
@@ -63,7 +59,7 @@ gap> IsoTypes := Collected(List(L, H -> StructureDescription(H)));
Main Functions
-In this section, we include all the main high-level functions provided to the User.
+In this section, we include all the main high-level functions provided to the user.
For advanced search methods in the lattice of normal subgroups, take a look at Chapter .
<#Include Label="LowIndexNormalSubs">
diff --git a/doc/lins_interface.xml b/doc/lins_interface.xml
index 17bd253..50a93c2 100644
--- a/doc/lins_interface.xml
+++ b/doc/lins_interface.xml
@@ -94,8 +94,7 @@ For this we revise the examples from the introduction as well as include new one
We compute all normal subgroups in D_{50},
the dihedral group of size 50.
n := 50;;
-gap> G := DihedralGroup(n);
+gap> G := DihedralGroup(50);
]]>
@@ -136,10 +135,7 @@ gap> IsoTypes := List(L, node -> StructureDescription(Grp(node)));
We compute all normal subgroups of index 5^2 = 25 in C_5^4,
the direct product of 4 copies of the cyclic group of order 5:
p := 5;;
-gap> d := 4;;
-gap> C := CyclicGroup(5);;
-gap> G := DirectProduct(ListWithIdenticalEntries(d, C));
+gap> G := ElementaryAbelianGroup(5^4);;
]]>
@@ -183,9 +179,8 @@ We compute a normal subgroup of index 3 \cdot 5 = 15 in
C_3 \times C_3 \times C_4 \times C_5,
a direct product of cyclic groups:
pList := [3, 3, 4, 5];;
-gap> G := DirectProduct(List(pList, p -> CyclicGroup(p)));
-
+gap> G := AbelianGroup([3, 3, 4, 5]);
+
gap> gr := LowIndexNormalSubgroupsSearchForIndex(G, 15, 1);
]]>