The investigation comes days after half of US nuclear missile wing was implicated in cheating; thus reflecting the "systematic" problems within the American defence system.
Admiral Jonathan Greenert, chief of naval operations, told reporters at a hurriedly convened news conference that he learned about it on Monday.
It took place in Charleston, South Carolina, at the Navy Nuclear Propulsion Command there.
"The propulsion exam was allegedly shared amongst some senior enlisted operators," Greenert said yesterday.
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Admiral John Richardson, director of the propulsion program, said this incident took place in its school.
"We have a one-year training programme that includes six months of classroom training, theoretical training, and six months of hands-on training. We do this in Charleston on two converted submarines that we use as training reactors to certify operators to report to the fleet," he said.
The cheating scandal at the Nuclear reactor facility comes days after the Air Force scandal in which some 92 officers at Malmstrom Air Force Base were involved. That case involved a proficiency test.