code: def _verify_centralizer(group, arg, centr=None):
      """
      Verify the centralizer of a group/set/element inside another group.
  
      This is used for testing ``.centralizer()`` from
      ``sympy.combinatorics.perm_groups``
  
      Examples
      ========
  
      >>> from sympy.combinatorics.named_groups import (SymmetricGroup,
      ... AlternatingGroup)
      >>> from sympy.combinatorics.perm_groups import PermutationGroup
      >>> from sympy.combinatorics.permutations import Permutation
      >>> from sympy.combinatorics.testutil import _verify_centralizer
      >>> S = SymmetricGroup(5)
      >>> A = AlternatingGroup(5)
      >>> centr = PermutationGroup([Permutation([0, 1, 2, 3, 4])])
      >>> _verify_centralizer(S, A, centr)
      True
  
      See Also
      ========
  
      _naive_list_centralizer,
      sympy.combinatorics.perm_groups.PermutationGroup.centralizer,
      _cmp_perm_lists
  
      """
      if centr is None:
          centr = group.centralizer(arg)
      centr_list = list(centr.generate_dimino(af=True))
      centr_list_naive = _naive_list_centralizer(group, arg, af=True)
      return _cmp_perm_lists(centr_list, centr_list_naive)
  
file_path: sympy/sympy/combinatorics/testutil.py
imports: from sympy.combinatorics import Permutation
  from sympy.combinatorics.util import _distribute_gens_by_base
label_desc: Use image node_id 4 for calling a global function with example usage: _verify_centralizer(group, arg, centr) and returns: _cmp_perm_lists