10 Infantry Regiment (USA) arrived in Iceland

First Elements (10th Inf and 46th FA Bn) arrived Iceland 16 Sep 41

Iceland was an important stepping stone between Europe and the New World. It could be used as a refueling base for aircraft, and as an air and sea attack base for the Axis. Hitler several times toyed with the idea of a descent upon the island and laid preliminary plans for it. To forestall such a move British troops, soon joined by a Canadian force, had landed (Invaded is more accurate) Iceland on 10 May 1940. Icelandic annoyance with the British and Canadian garrison, and British losses in the war, which made a withdrawal of the Iceland garrison seem desirable, plus American concern for the Atlantic sea lanes, combined to bring Iceland within the American defense orbit.

Source: http://www.ibiblio.org/hyperwar/USA/USA-WH-Guard/USA-WH-Guard-18.html