Binary transformation groups and topological fields
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914526480302080 |
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| author | Gevorgyan, Pavel S. |
| author_facet | Gevorgyan, Pavel S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_01626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Binary transformation groups and topological fields Gevorgyan, Pavel S. General Topology Group Theory Primary 54H15, Secondary 54H13, 12J10, 22A30 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. |
| title | Binary transformation groups and topological fields |
| topic | General Topology Group Theory Primary 54H15, Secondary 54H13, 12J10, 22A30 |
| url | https://arxiv.org/abs/2605.01626 |