The socialization of Generation Z takes place in the digital space. Digital socialization provides a special way of constructing the world of life and a specific way of acquiring ethical values among these young people. Socialization in the digital environment also promotes an anomie. The development of anomie in Generation Z leads to deviant behavior, which is manifested in unmotivated aggression, insulting other participants of communication in the digital environment. Along with anomie and deviation, Generation Z digital socialization is also characterized by opposite trends of institutionalization of the ethics of digital interaction. The practices of unethical behavior stimulate the emergence of discussions on the Internet about the limits of permissible and unacceptable behavior. This spontaneous discourse of digital ethics is extremely interesting from theoretical and practical points of view. Based on the natural ideas of individuals about ethical norms, it is possible to formulate a code of ethical conduct in the digital space. Such a code would not be coercive, but the very fact of its existence would have an impact on the behavior of individuals. The features of Generation Z that have been studied can be extremely useful for improving education. Understanding the specifics of these young people's world will allow them to develop more interesting courses and teaching methods. Knowledge of the genesis of ethical norms in the digital environment will allow effective translation of social constructive norms of behavior, ethical values into the young people communication.