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Se uno straniero sposato con un cittadino italiano può richiedere la cittadinanza?

Sì.

http://www.interno.gov.it/mininterno/export/sites/default/it/temi/cittadinanza/sottotema002.html

Certainly. The basic requirements are that you are the spouse of an Italian citizen and have been a legal resident of Italy for at least two years. Alternatively, if you live outside of Italy you must have been married for at least three years.