Update abelian group docs

docs/src/manual/abelian/elements.md

@@ -4,13 +4,13 @@ DocTestSetup = quote
     using Hecke
 end
 ```
-## Elements
+# Elements
 Elements in a finitely generated abelian group are of type `FinGenAbGroupElem`
 and are always given as a linear combination of the generators.
 Internally this representation is normliased to have a unique
 representative.
 
-### Creation
+## Creation
 In addition to the standard function `id`, `zero` and `one` that can be
 used to create the neutral element, we also support more targeted creation:
 ```@docs
@@ -22,22 +22,22 @@ rand(G::FinGenAbGroup)
 rand(G::FinGenAbGroup, B::ZZRingElem)
 parent(x::FinGenAbGroupElem)
 ```
-### Access
+## Access
 
 ```@docs
 getindex(x::FinGenAbGroupElem, i::Int)
 ```
 
-### Predicates
+## Predicates
 
 We have the standard predicates `iszero`, `isone` and `is_identity`
 to test an element for being trivial.
 
-### Invariants
+## Invariants
 ```@docs
 order(A::FinGenAbGroupElem)
 ```
-### Iterator
+## Iterator
 One can iterate over the elements of a finite abelian group.
 
 ```@repl

docs/src/manual/abelian/introduction.md

@@ -4,18 +4,14 @@ DocTestSetup = quote
     using Hecke
 end
 ```
-# [Abelian Groups](@id AbelianGroupLink2)
-
-Here we describe the interface to abelian groups in Hecke.
-
-## Introduction
+# [Introduction](@id AbelianGroupLink2)
 
 Within Hecke, abelian groups are of generic abstract type `GrpAb` which does not
 have to be finitely generated, $\mathbb Q/\mathbb Z$ is an example of a more
 general abelian group. Having said that, most of the functionality is
 restricted to abelian groups that are finitely presented as $\mathbb Z$-modules.
 
-### Basic Creation
+## Basic Creation
 
 Finitely presented (as $\mathbb Z$-modules) abelian groups are of type `FinGenAbGroup`
 with elements of type `FinGenAbGroupElem`. The creation is mostly via a relation
@@ -51,7 +47,7 @@ using Hecke # hide
 abelian_groups(8)
 ```
 
-### Invariants
+## Invariants
 ```@docs
 is_snf(A::FinGenAbGroup)
 number_of_generators(A::FinGenAbGroup)

docs/src/manual/abelian/maps.md

@@ -4,7 +4,7 @@ DocTestSetup = quote
     using Hecke
 end
 ```
-## Maps
+# Maps
 Maps between abelian groups are mainly of type `FinGenAbGroupHom`. They
 allow normal map operations such as `image`, `preimage`, `domain`, `codomain`
 and can be created in a variety of situations.

docs/src/manual/abelian/structural.md

@@ -4,7 +4,7 @@ DocTestSetup = quote
     using Hecke
 end
 ```
-## Structural Computations
+# Structural Computations
 Abelian groups support a wide range of structural operations such as
  - enumeration of subgroups
  - (outer) direct products
@@ -17,7 +17,7 @@ snf(A::FinGenAbGroup)
 Hecke.find_isomorphism(G, op, A::Hecke.GrpAb)
 ```
 
-### Subgroups and Quotients
+## Subgroups and Quotients
 ```@docs
 torsion_subgroup(G::FinGenAbGroup)
 sub(G::FinGenAbGroup, s::Vector{FinGenAbGroupElem})
@@ -81,21 +81,21 @@ The difference between `issubset =` $\subset$ and
 intersect(mG::FinGenAbGroupHom, mH::FinGenAbGroupHom)
 ```
 
-### Direct Products
+## Direct Products
 ```@docs
 direct_product(G::FinGenAbGroup...)
 canonical_injection(G::FinGenAbGroup, i::Int)
 canonical_projection(G::FinGenAbGroup, i::Int)
 flat(G::FinGenAbGroup)
 ```
 
-### Tensor Producs
+## Tensor Producs
 ```@docs
 tensor_product(G::FinGenAbGroup...)
 hom_tensor(G::FinGenAbGroup, H::FinGenAbGroup, A::Vector{ <: Map{FinGenAbGroup, FinGenAbGroup}})
 ```
 
-### Hom-Group
+## Hom-Group
 ```@docs
 hom(::FinGenAbGroup, ::FinGenAbGroup)
 ```

docs/src/manual/number_fields/conventions.md

@@ -1,4 +1,4 @@
-### Number fields
+# Conventions
 
 By an absolute number field we mean finite extensions of $\mathbf Q$, which is
 of type `AbsSimpleNumField` and whose elements are of type `AbsSimpleNumFieldElem`. Such an

docs/src/manual/orders/orders.md

@@ -100,7 +100,7 @@ All of the functions have a very similar interface: they return
 an abelian group and a map converting elements of the group
 into the objects required. The maps also
 allow a point-wise inverse to server as the *discrete logarithm* map.
-For more information on abelian group, see [here](@ref AbelianGroupLink2),
+For more information on abelian groups, see [here](@ref AbelianGroupLink2),
 for ideals, [here](@ref NfOrdIdlLink2).
 
 - [`torsion_unit_group(::AbsSimpleNumFieldOrder)`](@ref)