Сибирский журнал науки и технологий
ISSN 2587-6066

Vestnik sibsau
Vestnik sibsau
Vestnik sibsau
Vestnik sibsau

UDK 512.54 Doi: 10.31772/2587-6066-2018-19-3-432-437
MODELING OF THE LAYER STRUCTURE OF INFINTE GROUPS
V. I. Senashov, D. K. Belov*
Institute of Computational Modelling SB RAS 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation Siberian Federal University 79, Svobodny Av., Krasnoyarsk, 660041, Russian Federation *E-mail: white94@inbox.ru
Mathematical modeling of infinite discrete objects is possible if these objects satisfy any conditions of finiteness. If all the layers of elements in the group are finite, a functional description of the power of the layers for such a group is possible. A layer is a set of all elements of the group of the same order. For the first time the infinite layer-finite groups were investigated by S. N. Chernikov initially without a title, and then in his subsequent publications the name of layer-finite groups was fixed. The most intensive studies of the properties of layer-finite groups were carried out in the 1940s and 1950s by S. N. Chernikov, R. Baer, X. X. Muhammedzhan. The paper gives a functional description for some layer-finite groups. It is shown that primary layer-finite groups and layer-finite groups can be very well visualized in the case of two prime divisors of the orders of the elements of the group. For a primary case, it is convenient to use the usual graphical representation. In the case of two prime divisors of the orders of elements of a layer-finite group, visualization of the power functions of the layers by means of surfaces in three-dimensional space is carried out. For a larger number of simple order-divisors, an approach for modeling the layer structure of a complete layer-finite group using subgroup analysis is proposed. In this paper, we study the power functions of the layers for complete layer-finite groups and some finite extensions of these groups, and demonstrate their graphical representations.
Keywords: group, layer, power of layer, order, finite extension.
References

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Senashov Vladimir Ivanovich – Dr. Sc., professor, leading scientific worker, Institute of Computational Modelling SB RAS. E-mail: sen1112home@mail.ru.

Belov Dmitriy Konstantinovich – student of Siberian Federal University. E-mail: white94@inbox.ru.


  MODELING OF THE LAYER STRUCTURE OF INFINTE GROUPS