There were three campaigns fought by US forces in North Africa:
1. Egypt-Libya, 11June 42 / 12 Feb 43 2. Algeria-French Morocco, 9-11-42 3. Tunisia, 17 Nov 42 / 13 May 43.
These are the U.S. forces actually involved:
Fifth Army Headquarters. 1. II Corps 2. 1st Armored Division 3. 9th Infantry Division 4. 34th ID 5. 18th Regimental Combat Team (*) 6. 39th Regimental Combat Team (*) 7. 168th RCT.(*)
PLEASE NOTE: I can ID these units more precisly, including their roles in NA. Information in part from THE BATTLE FOR NORTH AFRICA, John Strawson, author, Charles Schriber's Sons, NYNY, publisher, (c) 1969. Excellent tome, with many combat photos.
Other information was found in WAR AS I KNEW IT, General George S. Patton, Jr., author, Houghton Miffin Company, Boston, MS, publisher, (c) 1947. Another excellent tome, with many maps and graphics.
Operation Torch was spearheaded by the Western Task Force , which included three task forces, derived from approximately 100 ships and personnel sailing in convoy from Norfolk, VA, and other personnel shipped from ports located in United Kingdom.
The task force included approximately 35,000 troops.
I hope this helps you in yourquest for "more light".