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

Версия для печати

Section: Physics. Mathematics. Informatics

UDC

512.541

Authors

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

Abstract

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.

Keywords

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.

References

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.