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Addition ⊕ on the Set of Nonnegative Integers. Pp. 155–162.

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Section: Physics. Mathematics. Informatics




Popov Ivan Nikolaevich, Institute of Mathematics, Information and Space Technologies, Northern (Arctic) Federal University named after M.V. Lomonosov (Arkhangelsk, Russia)


The paper considers an example of Abelian group with nonnegative integers as elements and an operation that is based on representation of a natural number as a sum of the degrees of a fixed number. It is shown that the constructed group contains subgroups of finite and infinite order. Using a graphical representation of linear mappings of finite subgroups of the group, we suggest a way of finding their subgroups.


group, subgroup, finite group, order of group, order of element of group, mapping of groups to themselves.

The full-text version of the article can be requested through the university’s library.


1. Kargopolov M.I., Merzlyakov Yu.I. Osnovy teorii grupp [Fundamentals of the Group Theory]. Moscow, 1982.
2. Kurosh A.G. Teoriya grupp [Group Theory]. Moscow, 1967.