Journal of the Australian Mathematical Society 4 (1964), 452–453The second paragraph should be deleted. The alleged commutator identity (3) is false and is certainly not due to Philip Hall. The correct form isas Dr. N. D. Gupta of Canberra has pointed out to me. According to Professor B. H. Neumann, this identity appeared in his (Professor Neumann's) thesis.Nevertheless the theorem is valid and the proof given is correct.