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.

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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.

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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.