The authors consider generalized norms for different systems of infinite and noncyclic subgroups in nonperiodic groups. Relations between these norms are established. The conditions under which the given norms are Dedekind, in particular, central, are studied.

The authors study finite 2-groups with the cyclic center and non-metacyclic non-Dedekind norm of Abelian non-cyclic subgroups. It is found out that such groups are cyclic or metacyclic extensions of their norms of Abelian non-cyclic subgroups. Their structure is described.

Author’s methodology of forming modeling skills involves 4 steps: Step 1 – the teacher step by step constructs the curve by means of cloud based service GeoGebra; Step 2 – the teacher offers a description-definition of the curve and provides a ready-made algorithm by which students model the curve independently in GeoGebra; Step 3 – the teacher offers an algorithm for constructing a curve model, and students need to characterize the properties of the curve or give its definition based on the results, Step 4 – students are offered definitions of curves that they have to model in GeoGebra). An example of realization of the author’s methodology is given, the pedagogical experiment on proof of its effectiveness is described.

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The authors raise the problem of informational influences on young people, who are often thoughtless consumers of Internet content, and actualize the need to train young people in the skills of information hygiene. According to the results of the student survey, the trustworthiness of young people to information content and the lack of ideas about the possible negative impact of information technologies, computer applications, social networks, and services on their health were confirmed. The author's special course on information hygiene is described as a tool for developing youth's ability to resist informational influences. It is shown how the tasks of the special course are achieved: to form a responsible attitude toward the consumption of information content; develop the ability to counteract destructive influences based on emotional colouring (psychological manipulations, propaganda, disinformation, etc.); develop practical skills to verify media products for their critical evaluation; to improve the skills of protecting one's own information space. The methods and tools of learning that contribute to solving the tasks are described. The results of the pedagogical experiment are presented, which confirm the effectiveness of the developed special course.