Step 1: Understanding administrative management. 
  
Henri Fayol is considered the father of administrative management theory. He proposed 14 principles of management, which focus on organizational structure, division of work, authority, discipline, unity of direction, and other management practices that help in the effective functioning of an organization. 
Step 2: Analyzing the options. 
  
(A) Fayol: Correct. Henri Fayol is the key proponent of administrative management and developed several principles to improve organizational management. 
  
(B) Taylor: Incorrect. Frederick Taylor is known for scientific management, which focuses on improving productivity through time and motion studies, not administrative management. 
  
(C) Terry: Incorrect. George R. Terry was known for his work in general management, but he is not credited with administrative management. 
  
(D) None of them: Incorrect. The correct answer is (A). 
Step 3: Conclusion. 
  
The correct answer is (A) Fayol, as he is the key proponent of administrative management.