Is there crime and punishment in a utopia?

The idea of a French Utopian society was popular in Russia during the mid-1800s. According to utopian beliefs, poverty was the cause of social ills, and it called for a redistribution of wealth through communal living, in planned communities in which members would be paid according to their contribution. Throughout crime and punishment, we see a struggle between the rich and the poor. In a utopia, there would be no struggle, as everyone would have a fair advantage of income. Therefore, there would logically be no crime.