sagemathgh-37850: Reverted changes from sagemath#36986

    
Reverted changes made in sagemath#36986

The bug in sagemath#36974 remains unsolved. Efforts are being made in sagemath#37744 to
resolve the bug.

Fixes  sagemath#37744
### 📝 Checklist

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- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies
    
URL: sagemath#37850
Reported by: Aman Moon
Reviewer(s):

src/sage/groups/abelian_gps/abelian_group.py

@@ -978,10 +978,6 @@ def gens_orders(self):
 
         TESTS::
 
-            sage: G, (g0, g1) = AbelianGroup(2, [48, 0]).objgens()
-            sage: G0 = G.subgroup([g0])  # optional - gap_package_polycyclic
-            sage: len(G0.gens()) == len(G0.gens_orders())  # optional - gap_package_polycyclic
-            True
             sage: F = AbelianGroup(3, [2], names='abc')
             sage: list(map(type, F.gens_orders()))
             [<class 'sage.rings.integer.Integer'>,
@@ -1661,7 +1657,7 @@ def __init__(self, ambient, gens, names="f", category=None):
             sage: B = A.subgroup([a^3, b, c, d, e^2]); B
             Multiplicative Abelian subgroup isomorphic to C4 x C5 x C5 x C7 generated by {b, c, d, e^2}
             sage: B.gens_orders()
-            (5, 5, 7, 4)
+            (4, 5, 5, 7)
             sage: A = AbelianGroup(4,[1009, 2003, 3001, 4001], names="abcd")
             sage: a,b,c,d = A.gens()
             sage: B = A.subgroup([a^3,b,c,d])
@@ -1686,7 +1682,7 @@ def __init__(self, ambient, gens, names="f", category=None):
             Multiplicative Abelian subgroup isomorphic to C2 x C3 x Z
              generated by {a, b^2, c}
             sage: F.gens_orders()
-            (3, 2, 0)
+            (2, 3, 0)
             sage: F.gens()
             (a, b^2, c)
             sage: F.order()
@@ -1712,20 +1708,16 @@ def __init__(self, ambient, gens, names="f", category=None):
         H = libgap(ambient).Subgroup(H_gens)
 
         invs = H.TorsionSubgroup().AbelianInvariants().sage()
-        gens_orders = tuple([ZZ(order_sage) for g in H.GeneratorsOfGroup()
-                            if (order_sage := g.Order().sage()) is not infinity])
-
         rank = len([1 for g in H.GeneratorsOfGroup()
                     if g.Order().sage() is infinity])
         invs += [0] * rank
 
-        gens_orders += (ZZ.zero(),) * rank
         self._abinvs = invs
         invs = tuple(ZZ(i) for i in invs)
 
         if category is None:
             category = Groups().Commutative().Subobjects()
-        AbelianGroup_class.__init__(self, gens_orders, names, category=category)
+        AbelianGroup_class.__init__(self, invs, names, category=category)
 
     def __contains__(self, x):
         """