Hello,
It is not clear from your question if you were ever convicted as a result of these arrests or when you first obtained your green card. This is information which is very important when you wish to submit an application with the USCIS for it lets one know if you will be eligible for naturalization and also, to ensure that you do not inadvertently end up in deportation proceedings due to your criminal convictions. The USCIS will review the past five (or three years if you got your green card through marriage and are still married to your U.S. citizen spouse) in particular to see if you are of good moral character. If one's arrests fall outside of the 3 or 5 years preceding your application, then it is possible to file for naturalization without worry.
Notes: This information is of a general nature and is not, nor is it intended to be legal advice. You should consult with an attorney for specific advice for your case.
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