The battalion that was on the Island was part of the South West Pacific Command, represented by the red A worn by Sam Austen and Kelvin during their service in Kuwait.
Fate of the soldiers
Richard was lying about killing all 18 of the soldiers to Faraday so that Faraday would report there was no one on the Island to rescue. In fact, some of the soldiers, like Cunningham, were on one of Jacob's lists and were taken into the Others.
It is highly unlikely that Cunningham could learn fluent Latin in a month. I think he was already one of the Hostiles when the U.S. Military arrived.
While I completely agree with you that he probably was already a Hostile, I would point out that in the 50s, the vast majority of schools in the united states, public or private, still required students to learn Latin (My father and three uncles, for example, all studied Latin while going to school in the late 40's and 50's.
I don't know anything about that since I'm from a whole different country, but Cunningham wasn't a student in the late 40s and 50s, was he? :)
Also, just because he learned classical Latin (what is usually taught in schools) does not mean that he would be able to speak conversational Latin, which I believe is what the Others use.
Not to mention the fact that he doesn't really seems to be affected by the death of his fellow comrades, so he probably was not a soldier.
The reason that the Army never came back to the island was that they were never able to find it again. My best guess would be that, in a short amount of time, it was located by the US, approved as a nuclear test site, and had a platoon sent there with jughead. However, very soon after they were killed, likely days, or even hours, the island moved again, making finding it impossible by the US Army, who only stumbled upon it by accident.--Master Tej (talk) 02:18, December 8, 2013 (UTC)
Who else in the Army knows about the island?
The Jughead test may not be an official Army project approved by the normal chain of command. It could be the work of an unofficial faction in the Army, or a classified project that only a few high-ranking officials know about. The wider Army would know that the soldiers and bomb are missing, but their destination and mission could be covered up, perhaps by faking a crashed or missing plane. But it would be difficult and risky for everyone who knew about the test to travel to the island, so probably there are still some people in the Army who know about the island, after the 18 who travelled with Jughead are killed.
People from the Army who knew about the Jughead test could have left the Army after 1954, perhaps becoming involved with the Hanso Foundation or another group interested in the Island.
Richard Alpert expects other people from the Army to come looking for the dead soldiers. This may be because some of the 18 said this would happen before they were killed, although it's a reasonable thing to expect anyway.
Alvar Hanso used the knowledge of his ancestors about the Island for his weapon industry. There, he could conduct nuclear test for the U.S. Army hidden from the Soviet Union. Therefore, the military only got to the Island on his behalf and were able to leave and return to it upon his instructions. It is also possible that Alvar was already aware of the hostiles, deploying the bomb to eliminate them. After this failed attempt, he changed his plan and developed the DI in order to regain control of the Island.
Why is the Army on the island?
If the Island is hidden in 1954, it would be a good place for nuclear tests, since they may be harder for other countries to detect than tests in normal locations. This would be even more useful for the military in later years, when the Soviet Union and other countries have satellite surveillance.
A place for secret nuclear tests would also allow the US Army to circumvent test ban treaties. By 1954 over 50 nuclear tests had been carried out worldwide, and there were already calls to end nuclear testing. In 1963 the Partial Test Ban Treaty, signed by the USA, USSR and UK, banned nuclear tests in the atmosphere, underwater and in space. If anyone who knows about the island is still in the US military after 1963, this would be an added incentive to return to the Island and conduct more atmospheric nuclear tests.
"Mattingly", "Jones" and "Cunningham" are candidates, and would have been brought to the island for the same reason as all the other candidates.