improvements for cosets (#4302)

* improvements for cosets

- access defining data via functions not fields
- rename `acting_domain` to `acting_group`
- improve documentation
- `in` for left/right cosets now delegates to a membership test in a group
- iterator for left/right cosets now uses a group iterator

* address a comment

* change parameterization of the `GroupCoset` type

Add the type of the *subgroup* as a parameter,
then we can prescribe a better `Base.IteratorSize(::Type{<:GroupCoset})`,
as proposed in #4289.

Note that in principle, we could omit the type of the *big group* from the
parameters since it is the `parent_type` of the element type parameter.
(The design of the `GroupCoset` type dates back to the times when
we thought that a group has the same type as its subgroups.
At the time when this idea was given up, I should have changed
`GroupCoset` to take the *subgroup* type as a parameter.)

* make `@inferred` happy

This was tricky:
The error messages were misleading, the problem occurred on a lower level.

Author: ThomasBreuer

docs/src/Groups/subgroups.md

@@ -112,24 +112,31 @@ subgroup_classes(G::GAPGroup)
 
 ```@docs
 GroupCoset
+group(C::GroupCoset)
+acting_group(C::GroupCoset)
+representative(C::GroupCoset)
 right_coset(H::GAPGroup, g::GAPGroupElem)
 left_coset(H::GAPGroup, g::GAPGroupElem)
-is_right(c::GroupCoset)
-is_left(c::GroupCoset)
-is_bicoset(C::GroupCoset)
-acting_domain(C::GroupCoset)
-representative(C::GroupCoset)
+is_right(C::GroupCoset)
+is_left(C::GroupCoset)
 right_cosets(G::GAPGroup, H::GAPGroup; check::Bool=true)
 left_cosets(G::GAPGroup, H::GAPGroup; check::Bool=true)
 right_transversal(G::T1, H::T2; check::Bool=true) where T1 <: GAPGroup where T2 <: GAPGroup
 left_transversal(G::T1, H::T2; check::Bool=true) where T1 <: GAPGroup where T2 <: GAPGroup
+is_bicoset(C::GroupCoset)
+```
+
+```@docs
 GroupDoubleCoset{T <: GAPGroup, S <: GAPGroupElem}
-double_coset(G::GAPGroup, g::GAPGroupElem, H::GAPGroup)
-double_cosets(G::T, H::GAPGroup, K::GAPGroup; check::Bool=true) where T <: GAPGroup
+group(C::GroupDoubleCoset)
 left_acting_group(C::GroupDoubleCoset)
 right_acting_group(C::GroupDoubleCoset)
 representative(C::GroupDoubleCoset)
+double_coset(G::GAPGroup, g::GAPGroupElem, H::GAPGroup)
+double_cosets(G::T, H::GAPGroup, K::GAPGroup; check::Bool=true) where T <: GAPGroup
+```
+
+```@docs
 order(C::Union{GroupCoset,GroupDoubleCoset})
 Base.rand(C::Union{GroupCoset,GroupDoubleCoset})
-intersect(V::AbstractVector{Union{<: GAPGroup, GroupCoset, GroupDoubleCoset}})
 ```

docs/src/Groups/tom.md

@@ -11,8 +11,8 @@ Therefore a table of marks is sometimes called a *Burnside matrix*.
 The table of marks of a finite group ``G`` is a matrix whose rows and columns
 are labelled by the conjugacy classes of subgroups of ``G`` and where for
 two subgroups ``H`` and ``K`` the ``(H, K)``-entry is the number of
-fixed points of ``K`` in the transitive action of ``G`` on the cosets of ``H``
-in ``G``.
+fixed points of ``K`` in the transitive action of ``G`` on the right cosets
+of ``H`` in ``G``.
 So the table of marks characterizes the set of all permutation representations
 of ``G``.
 Moreover, the table of marks gives a compact description of the