Can military members have guns on planes?

The Army deploys an entire Brigade of people at once. This is around 3-5,000 soldiers. They charter an entire fleet of commercial aircraft to do it. They will take off and land in secure military areas generally. So yes we bring our personal weapons on the plane, but we are not allowed to have any ammunition for them. There are No civilians on the plane, and it falls under different FAA regulations as it is then considered a "military" flight. If we are deploying as individuals on a normal flight, our weapons have to be in a locked case, inspected by TSA personnel and it is put underneath the plane.