Crumble the ground beef into a 4-5 quart dutch oven or roasting pan. Add the chopped onions and cook over medium-high heat for 5-6 minutes, stirring often, until the beef is brown.
Quarter and core the cabbage. Cut it crosswise in inch wide strips. You should have 8 cups. Add meat to the mixture. Cover and cook over medium heat for 5-7 minutes, stirring occassionally until the cabbage wilts.
Stir in tomatoes, sugar, vinegar, and salt. Bring to a boil, reduce heat, cover, and simmer, stirring occassionally for 10 minutes, or until the cabbage is tender.