introduce SubPcGroup (#3166)

docs/src/Groups/grouphom.md

@@ -166,7 +166,7 @@ isomorphism(G::GAPGroup, H::GAPGroup)
 ```
 
 ```@docs
-isomorphism(::Type{T}, G::GAPGroup) where T <: Union{PcGroup, PermGroup}
+isomorphism(::Type{T}, G::GAPGroup) where T <: Union{SubPcGroup, PermGroup}
 isomorphism(::Type{FinGenAbGroup}, G::GAPGroup)
 simplified_fp_group(G::FPGroup)
 ```

docs/src/Groups/quotients.md

@@ -11,7 +11,7 @@ Quotient groups in OSCAR can be defined using the instruction `quo` in two ways.
 
 * Quotients by normal subgroups.
 ```@docs
-quo(G::T, H::T) where T <: GAPGroup
+quo(G::GAPGroup, N::GAPGroup)
 ```
 
 * Quotients by elements.

docs/src/Groups/subgroups.md

@@ -11,14 +11,14 @@ The following functions are available in OSCAR for subgroup properties:
 
 ```@docs
 sub(G::GAPGroup, gens::AbstractVector{<:GAPGroupElem}; check::Bool = true)
-is_subset(H::T, G::T) where T <: GAPGroup
-is_subgroup(H::T, G::T) where T <: GAPGroup
-embedding(H::T, G::T) where T <: GAPGroup
-index(G::T, H::T) where T <: Union{GAPGroup, FinGenAbGroup}
-is_maximal_subgroup(H::T, G::T) where T <: GAPGroup
-is_normalized_by(H::T, G::T) where T <: GAPGroup
-is_normal_subgroup(H::T, G::T) where T <: GAPGroup
-is_characteristic_subgroup(H::T, G::T) where T <: GAPGroup
+is_subset(H::GAPGroup, G::GAPGroup)
+is_subgroup(H::GAPGroup, G::GAPGroup)
+embedding(H::GAPGroup, G::GAPGroup)
+index(G::GAPGroup, H::GAPGroup)
+is_maximal_subgroup(H::GAPGroup, G::GAPGroup; check::Bool = true)
+is_normalized_by(H::GAPGroup , G::GAPGroup)
+is_normal_subgroup(H::GAPGroup, G::GAPGroup)
+is_characteristic_subgroup(H::GAPGroup, G::GAPGroup; check::Bool = true)
 ```
 
 ## Standard subgroups
@@ -72,7 +72,7 @@ Usually it is more efficient to work with (representatives of) the
 underlying conjugacy classes of subgroups instead.
 
 ```@docs
-complements(G::T, N::T) where T <: GAPGroup
+complements(G::GAPGroup, N::GAPGroup)
 hall_subgroups
 low_index_subgroups
 maximal_subgroups
@@ -87,11 +87,11 @@ is_conjugate(G::GAPGroup, H::GAPGroup, K::GAPGroup)
 is_conjugate_with_data(G::GAPGroup, x::GAPGroupElem, y::GAPGroupElem)
 is_conjugate_with_data(G::GAPGroup, H::GAPGroup, K::GAPGroup)
 centralizer(G::GAPGroup, x::GAPGroupElem)
-centralizer(G::T, H::T) where T <: GAPGroup
+centralizer(G::GAPGroup, H::GAPGroup)
 normalizer(G::GAPGroup, x::GAPGroupElem)
-normalizer(G::T, H::T) where T<:GAPGroup
-core(G::T, H::T) where T<:GAPGroup
-normal_closure(G::T, H::T) where T<:GAPGroup
+normalizer(G::GAPGroup, H::GAPGroup)
+core(G::GAPGroup, H::GAPGroup)
+normal_closure(G::GAPGroup, H::GAPGroup)
 ```
 
 ```@docs
@@ -100,7 +100,7 @@ representative(G::GroupConjClass)
 acting_group(G::GroupConjClass)
 number_of_conjugacy_classes(G::GAPGroup)
 conjugacy_class(G::GAPGroup, g::GAPGroupElem)
-conjugacy_class(G::T, g::T) where T<:GAPGroup
+conjugacy_class(G::GAPGroup, H::GAPGroup)
 conjugacy_classes(G::GAPGroup)
 complement_classes
 hall_subgroup_classes
@@ -121,13 +121,13 @@ is_left(c::GroupCoset)
 is_bicoset(C::GroupCoset)
 acting_domain(C::GroupCoset)
 representative(C::GroupCoset)
-right_cosets(G::T, H::T; check::Bool=true) where T<: GAPGroup
-left_cosets(G::T, H::T; check::Bool=true) where T<: GAPGroup
-right_transversal(G::T, H::T; check::Bool=true) where T<: GAPGroup
-left_transversal(G::T, H::T; check::Bool=true) where T<: GAPGroup
+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
 GroupDoubleCoset{T <: GAPGroup, S <: GAPGroupElem}
-double_coset(G::T, g::GAPGroupElem{T}, H::T) where T<: GAPGroup
-double_cosets(G::T, H::T, K::T; check::Bool) where T<: GAPGroup
+double_coset(G::GAPGroup, g::GAPGroupElem, H::GAPGroup)
+double_cosets(G::T, H::GAPGroup, K::GAPGroup; check::Bool=true) where T <: GAPGroup
 left_acting_group(C::GroupDoubleCoset)
 right_acting_group(C::GroupDoubleCoset)
 representative(C::GroupDoubleCoset)

experimental/GModule/Brueckner.jl

@@ -57,7 +57,7 @@ function reps(K, G::Oscar.GAPGroup)
         r = R[pos]
         F = r.M
         @assert group(r) == s
-        rh = gmodule(group(r), [action(r, preimage(ms, x^h)) for x = gens(s)])
+        rh = gmodule(group(r), [action(r, preimage(ms, ms(x)^h)) for x = gens(s)])
         @hassert :BruecknerSQ 2 Oscar.GrpCoh.is_consistent(rh)
         l = Oscar.GModuleFromGap.hom_base(r, rh)
         @assert length(l) <= 1

experimental/SymmetricIntersections/src/representations.jl

@@ -630,7 +630,7 @@ function is_faithful(chi::Oscar.GAPGroupClassFunction, p::GAPGroupHomomorphism{T
   E = group(parent(chi))::T
   @req E === domain(p) "Incompatible underlying group of chi and domain of the cover p"
   @req is_projective(chi, p) "chi is not afforded by a p-projective representation"
-  Z = center(chi)[1]::T
+  Z = center(chi)[1]
   Q = kernel(p)[1]
   return Q.X == Z.X
 end
@@ -1070,8 +1070,8 @@ function _has_pfr(G::Oscar.GAPGroup, dim::Int)
     fff_gap = GG.IsomorphismPermGroup(H_gap)::GAP.GapObj
     E_gap = fff_gap(H_gap)::GAP.GapObj
   end
-  E = Oscar._get_type(E_gap)(E_gap)
-  H = Oscar._get_type(H_gap)(H_gap)
+  E = Oscar._oscar_group(E_gap)
+  H = Oscar._oscar_group(H_gap)
   fff = inv(GAPGroupHomomorphism(H, E, fff_gap))
   f = GAPGroupHomomorphism(H, G, f_gap)
   pschur = compose(fff, f)

gap/OscarInterface/gap/OscarInterface.gd

@@ -18,6 +18,12 @@ BindGlobal("IsPcGroupOrPcpGroup", IsGroup and CategoryCollections(IsPcElementOrP
 
 ############################################################################
 
+# Use a GAP property for caching whether a fp/pc/pcp group is a full group
+# and its stored generators are the generators for the defining presentation.
+DeclareProperty( "GroupGeneratorsDefinePresentation", IsGroup );
+
+############################################################################
+
 # Use GAP operations for the serialization of GAP objects.
 # (The methods will be Julia functions.)
 DeclareOperation( "SerializeInOscar", [ IsObject, IsObject ] );

gap/OscarInterface/gap/OscarInterface.gi

@@ -101,6 +101,32 @@ InstallMethod( IsGeneratorsOfMagmaWithInverses,
 
 ############################################################################
 
+InstallMethod( GroupGeneratorsDefinePresentation,
+   [ "IsPcGroup" ],
+   G -> GeneratorsOfGroup(G) = FamilyPcgs(G) );
+
+InstallMethod( GroupGeneratorsDefinePresentation,
+   [ "IsPcpGroup" ],
+   function( G )
+     local n, Ggens, i, w;
+
+     n:= One( G )!.collector![ PC_NUMBER_OF_GENERATORS ];
+     Ggens:= GeneratorsOfGroup( G );
+     if Length( Ggens ) <> n then
+       return false;
+     fi;
+     for i in [ 1 .. n ] do
+       w:= Ggens[i]!.word;
+       if not ( Length(w) = 2 and w[1] = i and w[2] = 1 ) then
+         return false;
+       fi;
+     od;
+     return true;
+   end );
+
+############################################################################
+
+
 Perform( Oscar._GAP_serializations,
          function( entry )
            InstallMethod( SerializeInOscar,

src/GAP/wrappers.jl

@@ -109,6 +109,7 @@ GAP.@wrap Identity(x::GapObj)::GapObj
 GAP.@wrap Image(x::Any)::GapObj
 GAP.@wrap Image(x::Any, y::Any)::GapObj
 GAP.@wrap ImagesRepresentative(x::GapObj, y::Any)::GAP.Obj
+GAP.@wrap ImagesSource(x::GapObj)::GapObj
 GAP.@wrap ImmutableMatrix(x::GapObj, y::GapObj, z::Bool)::GapObj
 GAP.@wrap IndependentGeneratorExponents(x::Any, y::Any)::GapObj
 GAP.@wrap Indeterminate(x::GapObj)::GapObj
@@ -192,6 +193,7 @@ GAP.@wrap IsomorphismFpGroupByGenerators(x::GapObj, y::GapObj)::GapObj
 GAP.@wrap IsomorphismFpGroupByPcgs(x::GapObj, y::GapObj)::GapObj
 GAP.@wrap IsOne(x::Any)::Bool
 GAP.@wrap IsPcGroup(x::Any)::Bool
+GAP.@wrap IsPcpGroup(x::Any)::Bool
 GAP.@wrap IsPerfectGroup(x::Any)::Bool
 GAP.@wrap IsPermGroup(x::Any)::Bool
 GAP.@wrap IsPGroup(x::Any)::Bool

src/Groups/GAPGroups.jl

@@ -186,7 +186,7 @@ function Base.rand(rng::Random.AbstractRNG, G::GAPGroup)
    return group_element(G, s)
 end
 
-function Base.rand(rng::Random.AbstractRNG, rs::Random.SamplerTrivial{Gr}) where Gr<:Oscar.GAPGroup
+function Base.rand(rng::Random.AbstractRNG, rs::Random.SamplerTrivial{Gr}) where Gr<:GAPGroup
    return rand(rng, rs[])
 end
 
@@ -234,6 +234,9 @@ end
 
 #We need a lattice of groups to implement this properly
 function _prod(x::T, y::T) where T <: GAPGroupElem
+#T not nec. same type,
+#T and for pc subgroups may need to go to the big group
+#T (write tests that model this situation)
   G = _common_parent_group(parent(x), parent(y))
   return group_element(G, GapObj(x)*GapObj(y))
 end
@@ -242,7 +245,7 @@ Base.:*(x::GAPGroupElem, y::GAPGroupElem) = _prod(x, y)
 
 ==(x::GAPGroup, y::GAPGroup) = GapObj(x) == GapObj(y)
 
-==(x::T, y::T) where T <: BasicGAPGroupElem = GapObj(x) == GapObj(y)
+==(x::BasicGAPGroupElem, y::BasicGAPGroupElem ) = GapObj(x) == GapObj(y)
 
 """
     one(G::GAPGroup) -> elem_type(G)
@@ -286,6 +289,7 @@ function Base.show(io::IO, G::FPGroup)
     end
   else
     print(io, "Finitely presented group")  # FIXME: actually some of these groups are *not* finitely presented
+#T introduce SubFPGroup
     if !is_terse(io)
     if has_order(G)
       if is_finite(G)
@@ -330,10 +334,11 @@ function Base.show(io::IO, G::PermGroup)
   end
 end
 
-function Base.show(io::IO, G::PcGroup)
+function Base.show(io::IO, G::Union{PcGroup,SubPcGroup})
   @show_name(io, G)
   @show_special(io, G)
-  print(io, "Pc group")
+  T = typeof(G) == PcGroup ? "Pc group" : "Subgroup of pc group"
+  print(io, T)
   if !is_terse(io)
     if isfinite(G)
       print(io, " of order ", order(G))
@@ -489,7 +494,7 @@ in general the length of this vector is not minimal.
 
 # Examples
 ```jldoctest
-julia> length(small_generating_set(abelian_group(PcGroup, [2,3,4])))
+julia> length(small_generating_set(abelian_group(SubPcGroup, [2,3,4])))
 2
 
 julia> length(small_generating_set(abelian_group(PermGroup, [2,3,4])))
@@ -512,7 +517,7 @@ Return a vector of minimal length of elements in `G` that generate `G`.
 
 # Examples
 ```jldoctest
-julia> length(minimal_generating_set(abelian_group(PcGroup, [2,3,4])))
+julia> length(minimal_generating_set(abelian_group(SubPcGroup, [2,3,4])))
 2
 
 julia> length(minimal_generating_set(abelian_group(PermGroup, [2,3,4])))
@@ -760,20 +765,21 @@ end
 
 # START subgroups conjugation
 """
-    conjugacy_class(G::T, H::T) where T<:Group -> GroupConjClass
+    conjugacy_class(G::Group, H::Group) -> GroupConjClass
 
 Return the subgroup conjugacy class `cc` of `H` in `G`, where `H` = `representative`(`cc`).
 """
-function conjugacy_class(G::T, g::T) where T<:GAPGroup
-   return GAPGroupConjClass(G, g, GAPWrap.ConjugacyClassSubgroups(GapObj(G),GapObj(g)))
+function conjugacy_class(G::GAPGroup, H::GAPGroup)
+#T _check_compatible
+   return GAPGroupConjClass(G, H, GAPWrap.ConjugacyClassSubgroups(GapObj(G),GapObj(H)))
 end
 
 function Base.rand(C::GroupConjClass{S,T}) where S where T<:GAPGroup
    return Base.rand(Random.GLOBAL_RNG, C)
 end
 
 function Base.rand(rng::Random.AbstractRNG, C::GroupConjClass{S,T}) where S where T<:GAPGroup
-   return _oscar_group(GAP.Globals.Random(GAP.wrap_rng(rng), C.CC), acting_group(C))
+   return _oscar_subgroup(GAP.Globals.Random(GAP.wrap_rng(rng), C.CC), acting_group(C))
 end
 
 """
@@ -842,9 +848,10 @@ julia> maximal_subgroup_classes(G)
 """
 @gapattribute function maximal_subgroup_classes(G::GAPGroup)
   L = Vector{GapObj}(GAP.Globals.ConjugacyClassesMaximalSubgroups(GapObj(G))::GapObj)
-  T = typeof(G)
+  TG = typeof(G)
+  TS = sub_type(TG)
   LL = [GAPGroupConjClass(G, _as_subgroup_bare(G, GAPWrap.Representative(cc)), cc) for cc in L]
-  return Vector{GAPGroupConjClass{T, T}}(LL)
+  return Vector{GAPGroupConjClass{TG, TS}}(LL)
 end
 
 """
@@ -921,7 +928,7 @@ Permutation group of degree 4 and order 3
 """
 function conjugate_group(G::T, x::GAPGroupElem) where T <: GAPGroup
   @req check_parent(G, x) "G and x are not compatible"
-  return _oscar_group(GAPWrap.ConjugateSubgroup(GapObj(G), GapObj(x)), G)
+  return _oscar_subgroup(GAPWrap.ConjugateSubgroup(GapObj(G), GapObj(x)), G)
 end
 
 Base.:^(H::GAPGroup, y::GAPGroupElem) = conjugate_group(H, y)
@@ -1152,7 +1159,7 @@ Return `N, f`, where `N` is the normalizer of `H` in `G`,
 i.e., the largest subgroup of `G` in which `H` is normal,
 and `f` is the embedding morphism of `N` into `G`.
 """
-normalizer(G::T, H::T) where T<:GAPGroup = _as_subgroup(G, GAPWrap.Normalizer(GapObj(G), GapObj(H)))
+normalizer(G::GAPGroup, H::GAPGroup) = _as_subgroup(G, GAPWrap.Normalizer(GapObj(G), GapObj(H)))
 
 """
     normalizer(G::Group, x::GAPGroupElem)
@@ -1169,7 +1176,7 @@ Return `C, f`, where `C` is the normal core of `H` in `G`,
 that is, the largest normal subgroup of `G` that is contained in `H`,
 and `f` is the embedding morphism of `C` into `G`.
 """
-core(G::T, H::T) where T<:GAPGroup = _as_subgroup(G, GAPWrap.Core(GapObj(G), GapObj(H)))
+core(G::GAPGroup, H::GAPGroup) = _as_subgroup(G, GAPWrap.Core(GapObj(G), GapObj(H)))
 
 """
     normal_closure(G::Group, H::Group)
@@ -1180,7 +1187,7 @@ and `f` is the embedding morphism of `N` into `G`.
 
 Note that `H` must be a subgroup of `G`.
 """
-normal_closure(G::T, H::T) where T<:GAPGroup = _as_subgroup(G, GAPWrap.NormalClosure(GapObj(G), GapObj(H)))
+normal_closure(G::GAPGroup, H::GAPGroup) = _as_subgroup(G, GAPWrap.NormalClosure(GapObj(G), GapObj(H)))
 
 # Note:
 # GAP admits `NormalClosure` also when `H` is not a subgroup of `G`,
@@ -1361,7 +1368,7 @@ an exception is thrown if `G` is not solvable.
 end
 
 @doc raw"""
-    complement_classes(G::T, N::T) where T <: GAPGroup
+    complement_classes(G::GAPGroup, N::GAPGroup)
 
 Return a vector of the conjugacy classes of complements
 of the normal subgroup `N` in `G`.
@@ -1383,20 +1390,20 @@ julia> G = dihedral_group(8)
 Pc group of order 8
 
 julia> complement_classes(G, center(G)[1])
-GAPGroupConjClass{PcGroup, PcGroup}[]
+GAPGroupConjClass{PcGroup, SubPcGroup}[]
 ```
 """
-function complement_classes(G::T, N::T) where T <: GAPGroup
+function complement_classes(G::T, N::GAPGroup) where T <: GAPGroup
    res_gap = GAP.Globals.ComplementClassesRepresentatives(GapObj(G), GapObj(N))::GapObj
    if length(res_gap) == 0
-     return GAPGroupConjClass{T, T}[]
+     return GAPGroupConjClass{T, sub_type(T)}[]
    else
      return [conjugacy_class(G, H) for H in _as_subgroups(G, res_gap)]
    end
 end
 
 @doc raw"""
-    complements(G::T, N::T) where T <: GAPGroup
+    complements(G::GAPGroup, N::GAPGroup)
 
 Return an iterator over the complements of the normal subgroup `N` in `G`.
 Very likely it is better to use [`complement_classes`](@ref) instead.
@@ -1409,7 +1416,7 @@ julia> describe(first(complements(G, derived_subgroup(G)[1])))
 "C2"
 ```
 """
-complements(G::T, N::T) where T <: GAPGroup = Iterators.flatten(complement_classes(G, N))
+complements(G::GAPGroup, N::GAPGroup) = Iterators.flatten(complement_classes(G, N))
 
 @doc raw"""
     complement_system(G::Group)
@@ -1910,7 +1917,7 @@ function map_word(g::PcGroupElem, genimgs::Vector; genimgs_inv::Vector = Vector(
   end
   gX = GapObj(g)
 
-  if GAP.Globals.IsPcGroup(GapObj(G))
+  if GAPWrap.IsPcGroup(GapObj(G))
     l = GAP.Globals.ExponentsOfPcElement(GAP.Globals.FamilyPcgs(GapObj(G)), gX)
   else  # GAP.Globals.IsPcpGroup(GapObj(G))
     l = GAP.Globals.Exponents(gX)
@@ -2269,7 +2276,12 @@ function describe(G::FPGroup)
 
    if !has_is_finite(G)
       # try to obtain an isomorphic permutation group, but don't try too hard
-      iso = GAP.Globals.IsomorphismPermGroupOrFailFpGroup(GapObj(G), 100000)::GapObj
+#TODO: With GAP 4.13.0, the prescribed bound 100000 will cause a test failure.
+#      This regression will hopefully be fixed in GAP 4.13.1,
+#      see https://github.com/gap-system/gap/issues/5697
+#      and https://github.com/gap-system/gap/pull/5698.
+#     iso = GAP.Globals.IsomorphismPermGroupOrFailFpGroup(GapObj(G), 100000)::GapObj
+      iso = GAP.Globals.IsomorphismPermGroupOrFailFpGroup(GapObj(G))::GapObj
       iso != GAP.Globals.fail && return describe(PermGroup(GAPWrap.Range(iso)))
    elseif is_finite(G)
       return describe(PermGroup(G))