I am US LPR and reside in US. I am planning to study the doctoral studies abroad, particularly in Finalnd. In the meanwhile, to protect my residency in US I would like to apply for re-entry permit. I was wondering whether I would be eligible to be admitted for re-entry permit I-131 or not?

I suggest, not knowing your particulars, you phone US immigratiion. Do you have any reason why you would not want to inquire ?

Certainly a case where you really want to get the right information from the right people... green card holders aren't allowed to spend most of their time abroad any longer as in years past.

File re-entry permit before you go, be very specific in the application, attached all supported documents is recommended. Each filing would be valid for 2 years, no question ask at any US port of entries, then you have to return to US and file the second one. In conclusion, you can go for 4 years, no longer than that.