code: def test_verify_centralizer():
      # verified by GAP
      S = SymmetricGroup(3)
      A = AlternatingGroup(3)
      triv = PermutationGroup([Permutation([0, 1, 2])])
      assert _verify_centralizer(S, S, centr=triv)
      assert _verify_centralizer(S, A, centr=A)
  
file_path: sympy/sympy/combinatorics/tests/test_testutil.py
imports: from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup, CyclicGroup
  from sympy.combinatorics.testutil import _verify_bsgs, _cmp_perm_lists, _naive_list_centralizer, _verify_centralizer, _verify_normal_closure
  from sympy.combinatorics.permutations import Permutation
  from sympy.combinatorics.perm_groups import PermutationGroup
  from sympy.core.random import shuffle
label_desc: Use image node_id 4 for calling a global function with example usage: test_verify_centralizer() without return types