Abstract
We define a Kulakov algebraic system as a three-sorted algebraic system satisfying the axioms of a physical structure. We prove a strong version of Ionin’s Theorem on the equivalence of the rank \( (2,2) \) physical structure to the structure of an abstract group. We consider nongroup Kulakov algebraic systems and characterize Kulakov algebraic systems over arbitrary groups.
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Notes
Along with the term a physical structure the term a phenomenological symmetric geometry of two sets is used, or briefly a geometry of two sets.
Sometimes it is called multibase or heterogeneous.
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Funding
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0011).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 6, pp. 1357–1368. https://doi.org/10.33048/smzh.2021.62.611
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Neshchadim, M.V., Simonov, A.A. Kulakov Algebraic Systems on Groups. Sib Math J 62, 1100–1109 (2021). https://doi.org/10.1134/S0037446621060112
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DOI: https://doi.org/10.1134/S0037446621060112