In discussing this, your first job should be to distinguish between facts and myths. The actual reality, for the past century, has been that immigrants, on the average, have been more law-abiding than American citizens, and less likely to commit and be convicted of crimes. On the other hand, a story, for example, of a tailor and his wife who moved from Italy to the United States, opening a dry cleaning and tailoring shop, and had a couple of kids who grew up and went to college doesn't make for a thrilling movie, while stories of Mafia bosses are dramatic and exciting.
Like most immigrant communities, the Italian-Americans of the early twentieth century were, overall, hard working and law abiding, although, as within any group, there were among them a few who turned to crime. The precipitating factor for the growth of organized crime was 18th Amendment to the U.S. Constitution, or Prohibition, which made the sale of alcohol illegal. The response to this was a growth in organized crime, both among ethnic groups in urban centers and the renowned moonshiners of Appalachia. The Sicilian Mafia, an existing organized crime group in Italy that was under pressure from the fascist dictator Mussolini, saw this as an opportunity to expand operations into the United States.
Thus your thesis might focus on how Prohibition led to the growth of organized crime, and how after alcohol was legalized, and profits from bootlegging disappeared, organized crime moved into dealing other illegal substances and other activities. You might conclude by speculating on how legalization and regulation of drugs may actually reduce organized crime by taking away its most profitable business.