Groups of binary transformations and topological fields
https://doi.org/10.22405/2226-8383-2025-26-4-271-287
Abstract
The notion of a semitransitive binary action of a group 𝐺 on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive
distributive binary 𝐺-spaces and topological fields whose multiplicative group is isomorphic to 𝐺. This result yields an equivalence between the category of semitransitive distributive binary 𝐺-spaces and the category of topological fields with multiplicative group 𝐺.
As applications of the duality theorem, two important results are established. It is shown that a finite group can act semitransitively, distributively, and binarily only on finite sets whose cardinality is a power of a prime number. A complete characterization of those groups that can appear as multiplicative groups of topological fields is also obtained.
About the Author
Pavel Samvelovich Gevorgyan
Moscow Pedagogical State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
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Review
For citations:
Gevorgyan P.S. Groups of binary transformations and topological fields. Chebyshevskii Sbornik. 2025;26(4):271-287. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-271-287
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