I married to us citizen, we are living & working abroad in profitable company, if I got my green card can I live abroad? and can I apply for citizenship after 3 years?
Note: My wife is us citizen and she is living abroad to help her mather.
Whether you could apply for naturalization based on your marriage to a USC will depend on how much time you have spent outside of the country. Remember, you have to comply with continuous residency and physical presence requirements of naturalization. From the facts stated, if you have resided and been physically present outside of the US for the past three years (I am unclear on this from the facts), you probably are not eligible for naturalization.
You need to consult with an immigration attorney immediately to discuss your status and future.
I agree with my colleague. You should return immediately and be prepared to be examined upon entry and possibility of revoking your green card. You'd better have good reasons for your staying abroad. Hopefully you've paid U.S. taxes on your world-wide income, filed U.S. income tax returns, kept your state driver's license current and maintained other proof of having a domicile here in the U.S.A. Consult with your immigration lawyer.
The idea of being a permanent resident is that you are residing in the United States. in order to naturalize you must satisfy certain physical presence and continuous residence requirements. Consult with an experienced immigration attorney who can review the facts of your case and advise you how best to proceed.