fix suggested details

src/sage/categories/action.pyx

@@ -381,10 +381,10 @@ cdef class InverseAction(Action):
     def __init__(self, Action action):
         G = action.G
         try:
-            from sage.groups.group import is_Group
+            from sage.groups.group import Group
             # We must be in the case that parent(~a) == parent(a)
             # so we can invert in _call_ code below.
-            if (is_Group(G) and G.is_multiplicative()) or G.is_field():
+            if (isinstance(G, Group) and G.is_multiplicative()) or G.is_field():
                 Action.__init__(self, G, action.underlying_set(), action._is_left)
                 self._action = action
                 return

src/sage/groups/additive_abelian/additive_abelian_group.py

@@ -6,11 +6,10 @@
 major differences are in the way elements are printed.
 """
 
-from sage.structure.parent import Parent
-from sage.modules.fg_pid.fgp_module import FGP_Module_class
+from sage.categories.commutative_additive_groups import CommutativeAdditiveGroups
 from sage.modules.fg_pid.fgp_element import FGP_Element
+from sage.modules.fg_pid.fgp_module import FGP_Module_class
 from sage.rings.integer_ring import ZZ
-from sage.categories.commutative_additive_groups import CommutativeAdditiveGroups
 
 
 def AdditiveAbelianGroup(invs, remember_generators=True):
@@ -202,7 +201,7 @@ def _repr_(self) -> str:
 # since we want to inherit things like __hash__ from there rather than the
 # hyper-generic implementation for abstract abelian groups.
 
-class AdditiveAbelianGroup_class(FGP_Module_class, Parent):
+class AdditiveAbelianGroup_class(FGP_Module_class):
     r"""
     An additive abelian group, implemented using the `\ZZ`-module machinery.
 
@@ -224,9 +223,12 @@ def __init__(self, cover, relations):
             Additive abelian group isomorphic to Z
             sage: G == loads(dumps(G))
             True
+            sage: G.category()
+            Category of modules over Integer Ring
+            sage: G in CommutativeAdditiveGroups()
+            True
         """
         FGP_Module_class.__init__(self, cover, relations)
-        Parent.__init__(self, category=CommutativeAdditiveGroups())
 
     def _repr_(self):
         r"""

src/sage/groups/group.pyx

@@ -16,12 +16,12 @@ Base class for groups
 #
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
-
-from sage.structure.parent cimport Parent
+from sage.misc.superseded import deprecation
 from sage.rings.infinity import infinity
+from sage.structure.parent cimport Parent
 
 
-def is_Group(x) -> bool:
+def is_Group(x):
     """
     Return whether ``x`` is a group object.
 
@@ -38,10 +38,13 @@ def is_Group(x) -> bool:
         sage: F.<a,b> = FreeGroup()                                                     # needs sage.groups
         sage: from sage.groups.group import is_Group
         sage: is_Group(F)                                                               # needs sage.groups
+        doctest:warning...DeprecationWarning: use instead G in Groups()
+        See https://github.com/sagemath/sage/issues/37449 for details.
         True
         sage: is_Group("a string")
         False
     """
+    deprecation(37449, 'use instead G in Groups()')
     return isinstance(x, Group)
 
 

src/sage/groups/old.pyx

@@ -1,5 +1,5 @@
 """
-Deprecated Base class for groups
+Deprecated base class for groups
 """
 
 # ****************************************************************************
@@ -18,7 +18,7 @@ Deprecated Base class for groups
 # ****************************************************************************
 
 doc = """
-Deprecated Base class for all groups
+Deprecated base class for all groups
 """
 import sage.rings.integer_ring
 from sage.misc.superseded import deprecation