How are students who travel to Israel to study for a year permitted to leave the land and return to America? Is this not clearly forbidden by Halacha? What about others? Sources please. Thank you,

Rambam (Hilchot M’lachim 5 9) forbids leaving Eretz Yisrael even temporarily except for a limited number of reasons- to study Torah etc. and once the purpose has been achieved, to return to Israel. To leave Israel to dwell permanently outside its borders is forbidden except when there is a famine. The implication, however, is that someone who already dwells permanently outside of Israel and is just visiting Israel is not violating this prohibition (see Shu”t Maharitatz of Harav Yom Tov Zahalon who lived in Zfat 450 years ago, teshuva 85, who addresses this directly). There is, however, an obligation on all Jews whether at present in Israel or not, to live in Israel. Rambam (Hilchot Melachim 5 12) writes that one should live in the Land of Israel even in a city that is mostly non-Jewish and prefer this to living outside of Israel in a Jewish city.