Add hasgens(G::GAPGroup)

docs/src/Groups/basics.md

@@ -27,6 +27,7 @@ one(x::GAPGroup)
 one(x::GAPGroupElem)
 isfiniteorder(x::GAPGroupElem)
 gens(::GAPGroup)
+hasgens(::GAPGroup)
 ngens(G::GAPGroup)
 gen(::GAPGroup, i::Int)
 Base.rand(G::GAPGroup)

src/Groups/GAPGroups.jl

@@ -25,7 +25,7 @@ export
     frattini_subgroup, hasfrattini_subgroup, setfrattini_subgroup,
     gap_perm, # HACK
     gen,
-    gens,
+    gens, hasgens,
     hall_subgroup,
     hall_subgroups_representatives,
     hall_system, hashall_system, sethall_system,
@@ -368,6 +368,28 @@ function gens(G::GAPGroup)
    return res
 end
 
+"""
+    hasgens(G::Group)
+
+Return whether generators for the group `G` are known.
+
+# Examples
+```jldoctest
+julia> F = free_group(2)
+<free group on the generators [ f1, f2 ]>
+
+julia> hasgens(F)
+true
+
+julia> H = derived_subgroup(F)[1]
+Group(<free, no generators known>)
+
+julia> hasgens(H)
+false
+```
+"""
+hasgens(G::GAPGroup) = GAP.Globals.HasGeneratorsOfGroup(G.X)::Bool
+
 """
     gen(G::GAPGroup, i::Int)
 

src/imports.jl

@@ -96,6 +96,7 @@ import AbstractAlgebra:
 
 import AbstractAlgebra.GroupsCore
 import AbstractAlgebra.GroupsCore:
+    hasgens,
     isfiniteorder,
     istrivial