Final answer:
Section 19 of the OSH Act of 1970 requires Army managers to have a safety program in place, in accordance with the standards set by OSHA.
Step-by-step explanation:
The publication that establishes the basic requirement for Army managers to have a safety program in place is Section 19 of the OSH Act of 1970. This section specifically outlines the responsibilities federal agencies have in creating and maintaining safety programs. It requires agencies, including the Army, to establish and maintain an effective and comprehensive occupational safety and health program that is consistent with the standards promulgated by the Occupational Safety and Health Administration (OSHA). Moreover, the Job Safety and Health: It's the Law Poster provides a clear representation of employees' safety rights that has to be adhered to by all employers, reinforcing the requirements of the OSH Act.