Can I go back t the US by permanent residence?

Although not clear from your question, it sounds like are a foreign national living outside of the United States, you believe you may be eligible to consular process and ultimately become a Lawful Permanent Resident, and you are wondering whether your entry into the U.S. with an F1 visa combined with your failure to attend the designated school, with stand in the way of qualifying to become a Permanent Resident. If that is a correct understanding of your question, then significantly more information is needed for a legal analysis. That may include, for example, knowing the reason you did not attend the school, the period of time you may have been unlawfully present in the U.S., the basis upon which you now believe you should be eligible for immigration benefits, etc. There really is no substitute for engaging an immigration attorney who, after learning all of the relevant information about you and your immigration-related history, could advise you about immigration eligibilities, options and strategies.