feat: subgroup enumeration with no subgroups (#1670)

Author: thofma

docs/src/index.md

@@ -46,7 +46,7 @@ If your research depends on computations done with Hecke, please consider giving
 - Claus Fieker, William Hart, Tommy Hofmann and Fredrik Johansson, [Nemo/Hecke: Computer Algebra and Number Theory Packages
   for the Julia Programming Language](https://doi.acm.org/10.1145/3087604.3087611). In: Proceedings of ISSAC '17, pages 157–164, New York, NY, USA, 2017. ACM.
 
-```bib
+```
 @inproceedings{nemo,
     author = {Fieker, Claus and Hart, William and Hofmann, Tommy and Johansson, Fredrik},
      title = {Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language},

src/GrpAb/SubgroupEnum.jl

@@ -875,6 +875,13 @@ end
 # Same as above but now allow a function to be applied to the output
 function _subgroups(G::FinGenAbGroup; subtype = [-1], quotype = [-1], order = -1,
                                     index = -1, fun = sub)
+  if !is_divisible_by(Hecke.order(G), order) || # the -1 default is ok
+     !is_divisible_by(Hecke.order(G), index) ||
+     (subtype != [-1] && !has_quotient(G, subtype)) ||
+     (quotype != [-1] && !has_quotient(G, quotype))
+    return ()
+  end
+
   return ( fun(G, convert(Vector{FinGenAbGroupElem}, z)) for z in _subgroups_gens(G, subtype, quotype, order, index))
 end
 
@@ -919,14 +926,6 @@ function subgroups(G::FinGenAbGroup; subtype = :all,
 
   options = Int16[ subtype != :all, quotype != :all, order != -1, index != -1]
 
-  if mod(Hecke.order(G), index) != 0
-    error("Index must divide the group order")
-  end
-
-  if mod(Hecke.order(G), order) != 0
-    error("Index must divide the group order")
-  end
-
   if sum(options) > 1
     error("Currently only one non-default parameter is supported.")
   end

test/GrpAb/SubgroupEnum.jl

@@ -220,4 +220,15 @@
       @test all([order(t[1]) == 7*3 for t in T])
     end
   end
+
+  # test for no subgroups
+
+  G = abelian_group([9, 3, 3])
+  @test length(collect(subgroups(G; index = 2))) == 0
+  @test length(collect(subgroups(G; order = 10001323))) == 0
+  @test length(collect(subgroups(G; subtype = [6, 6, 6]))) == 0
+  @test length(collect(subgroups(G; quotype = [6, 6, 6]))) == 0
+
+  G = abelian_group([2])
+  @test length(collect(subgroups(G; quotype = [3]))) == 0
 end