support group properties for character tables (oscar-system#3449)

and character value access by class names

Author: ThomasBreuer

docs/src/Groups/basics.md

@@ -70,17 +70,17 @@ is_finite(G::GAPGroup)
 is_trivial(G::GAPGroup)
 is_cyclic(G::GAPGroup)
 is_abelian(G::GAPGroup)
-is_elementary_abelian
-is_pgroup
-is_pgroup_with_prime
-is_nilpotent
-is_supersolvable
-is_solvable
-is_perfect
+is_elementary_abelian(G::GAPGroup)
+is_pgroup(G::GAPGroup)
+is_pgroup_with_prime(::Type{T}, G::GAPGroup) where T <: IntegerUnion
+is_nilpotent(G::GAPGroup)
+is_supersolvable(G::GAPGroup)
+is_solvable(G::GAPGroup)
+is_perfect(G::GAPGroup)
 is_simple(G::GAPGroup)
 is_almost_simple(G::GAPGroup)
-is_quasisimple
-is_sporadic_simple
+is_quasisimple(G::GAPGroup)
+is_sporadic_simple(G::GAPGroup)
 is_finitely_generated(G::GAPGroup)
 ```
 

docs/src/Groups/group_characters.md

@@ -143,6 +143,24 @@ trivial_character(tbl::GAPGroupCharacterTable)
 regular_character(tbl::GAPGroupCharacterTable)
 ```
 
+The following properties of a group can be read off from its
+character table.
+Therefore it is supported to call these functions with a character table.
+
+```@docs
+is_abelian(tbl::GAPGroupCharacterTable)
+is_almost_simple(tbl::GAPGroupCharacterTable)
+is_cyclic(tbl::GAPGroupCharacterTable)
+is_elementary_abelian(tbl::GAPGroupCharacterTable)
+is_nilpotent(tbl::GAPGroupCharacterTable)
+is_perfect(tbl::GAPGroupCharacterTable)
+is_quasisimple(tbl::GAPGroupCharacterTable)
+is_simple(tbl::GAPGroupCharacterTable)
+is_solvable(tbl::GAPGroupCharacterTable)
+is_sporadic_simple(tbl::GAPGroupCharacterTable)
+is_supersolvable(tbl::GAPGroupCharacterTable)
+```
+
 ## Construct group characters from groups
 
 ```@docs

src/Groups/group_characters.jl

@@ -1642,6 +1642,212 @@ function known_class_fusions(tbl::GAPGroupCharacterTable)
 end
 
 
+##############################################################################
+##
+##  mathematical properties of a group that can be read off from its
+##  character table
+##
+
+"""
+    is_abelian(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of an abelian group,
+see [`is_abelian(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_abelian(character_table("A5"))
+false
+
+julia> is_abelian(character_table("C2"))
+true
+```
+"""
+@gapattribute is_abelian(tbl::GAPGroupCharacterTable) = GAP.Globals.IsAbelian(GAPTable(tbl))::Bool
+
+
+"""
+    is_almost_simple(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of an almost simple group,
+see [`is_almost_simple(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_almost_simple(character_table("S5"))
+true
+
+julia> is_almost_simple(character_table("S4"))
+false
+```
+"""
+@gapattribute is_almost_simple(tbl::GAPGroupCharacterTable) = GAP.Globals.IsAlmostSimple(GAPTable(tbl))::Bool
+
+
+"""
+    is_cyclic(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of a cyclic group,
+see [`is_cyclic(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_cyclic(character_table("C2"))
+true
+
+julia> is_cyclic(character_table("S4"))
+false
+```
+"""
+@gapattribute is_cyclic(tbl::GAPGroupCharacterTable) = GAP.Globals.IsCyclic(GAPTable(tbl))::Bool
+
+
+"""
+    is_elementary_abelian(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of
+an elementary abelian group,
+see [`is_elementary_abelian(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_elementary_abelian(character_table("C2"))
+true
+
+julia> is_elementary_abelian(character_table("S4"))
+false
+```
+"""
+@gapattribute is_elementary_abelian(tbl::GAPGroupCharacterTable) = GAP.Globals.IsElementaryAbelian(GAPTable(tbl))::Bool
+
+
+"""
+    is_nilpotent(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of a nilpotent group,
+see [`is_nilpotent(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_nilpotent(character_table("C2"))
+true
+
+julia> is_nilpotent(character_table("S4"))
+false
+```
+"""
+@gapattribute is_nilpotent(tbl::GAPGroupCharacterTable) = GAP.Globals.IsNilpotent(GAPTable(tbl))::Bool
+
+
+"""
+    is_perfect(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of a perfect group,
+see [`is_perfect(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_perfect(character_table("A5"))
+true
+
+julia> is_perfect(character_table("S4"))
+false
+```
+"""
+@gapattribute is_perfect(tbl::GAPGroupCharacterTable) = GAP.Globals.IsPerfect(GAPTable(tbl))::Bool
+
+
+"""
+    is_quasisimple(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of a quasisimple group,
+see [`is_quasisimple(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_quasisimple(character_table("A5"))
+true
+
+julia> is_quasisimple(character_table("S4"))
+false
+```
+"""
+@gapattribute is_quasisimple(tbl::GAPGroupCharacterTable) = GAP.Globals.IsQuasisimple(GAPTable(tbl))::Bool
+
+
+"""
+    is_simple(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of a simple group,
+see [`is_simple(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_simple(character_table("A5"))
+true
+
+julia> is_simple(character_table("S4"))
+false
+```
+"""
+@gapattribute is_simple(tbl::GAPGroupCharacterTable) = GAP.Globals.IsSimple(GAPTable(tbl))::Bool
+
+
+"""
+    is_solvable(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of a solvable group,
+see [`is_solvable(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_solvable(character_table("A5"))
+false
+
+julia> is_solvable(character_table("S4"))
+true
+```
+"""
+@gapattribute is_solvable(tbl::GAPGroupCharacterTable) = GAP.Globals.IsSolvable(GAPTable(tbl))::Bool
+
+
+"""
+    is_sporadic_simple(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of
+a sporadic simple group,
+see [`is_sporadic_simple(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_sporadic_simple(character_table("A5"))
+false
+
+julia> is_sporadic_simple(character_table("M11"))
+true
+```
+"""
+@gapattribute is_sporadic_simple(tbl::GAPGroupCharacterTable) = GAP.Globals.IsSporadicSimple(GAPTable(tbl))::Bool
+
+
+"""
+    is_supersolvable(tbl::GAPGroupCharacterTable)
+
+Return whether `tbl` is the ordinary character table of a supersolvable group,
+see [`is_supersolvable(G::GAPGroup)`](@ref).
+
+# Examples
+```jldoctest
+julia> is_supersolvable(character_table("A5"))
+false
+
+julia> is_supersolvable(character_table("S3"))
+true
+```
+"""
+@gapattribute is_supersolvable(tbl::GAPGroupCharacterTable) = GAP.Globals.IsSupersolvable(GAPTable(tbl))::Bool
+
+
 #############################################################################
 ##
 ##  class functions (and characters)
@@ -2061,12 +2267,19 @@ Nemo.degree(::Type{QQAbElem}, chi::GAPGroupClassFunction) = values(chi)[1]::QQAb
 
 Nemo.degree(::Type{T}, chi::GAPGroupClassFunction) where T <: IntegerUnion = T(Nemo.degree(ZZRingElem, chi))::T
 
-# access character values
+# access character values by position
 function Base.getindex(chi::GAPGroupClassFunction, i::Int)
   vals = GAPWrap.ValuesOfClassFunction(chi.values)
   return QQAbElem(vals[i])
 end
 
+# access character values by class name
+function Base.getindex(chi::GAPGroupClassFunction, nam::String)
+  i = findfirst(is_equal(nam), class_names(parent(chi)))
+  @req i != nothing "$nam is not a class name"
+  return chi[i]
+end
+
 # arithmetic with class functions
 function Base.:(==)(chi::GAPGroupClassFunction, psi::GAPGroupClassFunction)
     @req parent(chi) === parent(psi) "character tables must be identical"

test/Groups/group_characters.jl

@@ -852,6 +852,7 @@ end
   @test chi isa Oscar.GAPGroupClassFunction
   @test chi[4] == t[2,4]
   @test [chi[i] for i in 1:5] == values(chi)
+  @test [chi[nam] for nam in class_names(t)] == values(chi)
   @test [2*chi[i] for i in 1:5] == values(chi + chi)
   @test [chi[i]^2 for i in 1:5] == values(chi * chi)
   @test [chi[i]^2 for i in 1:5] == values(chi^2)
@@ -1281,3 +1282,18 @@ end
     end
   end
 end
+
+@testset "read off group properties from character tables" begin
+  t = character_table("A5")
+  @test ! is_abelian(t)
+  @test is_almost_simple(t)
+  @test ! is_cyclic(t)
+  @test ! is_elementary_abelian(t)
+  @test ! is_nilpotent(t)
+  @test is_perfect(t)
+  @test is_quasisimple(t)
+  @test is_simple(t)
+  @test ! is_solvable(t)
+  @test ! is_sporadic_simple(t)
+  @test ! is_supersolvable(t)
+end