Final answer:
Alexander the Great encouraged his generals to marry Persian noblewomen as part of his strategy to integrate Greek and Persian cultures and stabilize his empire.
Step-by-step explanation:
One custom that Alexander the Great encouraged among his generals was the practice of marrying Persian noblewomen. This policy was part of a broader strategy to integrate the Greek and Persian cultures, aiming to establish a unified empire.
Alexander sought not to devastate but to rule as the new "Great King" and earn the respect and allegiance of the Persian people. By marrying into Persian nobility, his officers were expected to help fuse the two civilizations together, creating strong ties and alliances that would stabilize his vast empire.