On the Group of Computable Automorphisms of the Linear Order of the Reals Full article
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Twenty Years of Theoretical and Practical Synergies : 20th Conference on Computability in Europe 08-12 Jul 2024 , Amsterdam |
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| Source | Twenty Years of Theoretical and Practical Synergies : 20th Conference on Computability in Europe, CiE 2024, Amsterdam, The Netherlands, July 8–12, 2024: Proceedings Compilation, Springer Cham. 2024. 462 c. ISBN 978-3-031-64309-5. |
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| Journal |
Lecture Notes in Computer Science
ISSN: 0302-9743 , E-ISSN: 1611-3349 |
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| Output data | Year: 2024, Volume: 14773, Pages: 405-419 Pages count : 15 DOI: 10.1007/978-3-031-64309-5_32 | ||
| Tags | automorphism groups, ordered permutation groups, lattice-ordered groups, computability theory, computable analysis | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Mathematical Center in Akademgorodok | 075-15-2022-282 |
Abstract:
We study the group Autc(R) of computable automorphisms of the linear order of the reals. It is shown that this group shares several common properties with the group Autc(Q) of computable automorphisms of the rationals: they both are not divisible and each of them has exactly three nontrivial normal subgroups. Each of these groups contains an element that is not conjugate with its square. However, Autc(R) also possesses properties that are not present in Autc(Q): Autc(R) contains a bump that is not conjugate with its square and, for every c.e. real z, Autc(R) contains a bump with upper boundary point z.
Cite:
Kornev R.
On the Group of Computable Automorphisms of the Linear Order of the Reals
In compilation Twenty Years of Theoretical and Practical Synergies : 20th Conference on Computability in Europe, CiE 2024, Amsterdam, The Netherlands, July 8–12, 2024: Proceedings. – Springer Cham., 2024. – C.405-419. – ISBN 978-3-031-64309-5. DOI: 10.1007/978-3-031-64309-5_32 WOS Scopus OpenAlex
On the Group of Computable Automorphisms of the Linear Order of the Reals
In compilation Twenty Years of Theoretical and Practical Synergies : 20th Conference on Computability in Europe, CiE 2024, Amsterdam, The Netherlands, July 8–12, 2024: Proceedings. – Springer Cham., 2024. – C.405-419. – ISBN 978-3-031-64309-5. DOI: 10.1007/978-3-031-64309-5_32 WOS Scopus OpenAlex
Dates:
| Published print: | Jul 2, 2024 |
| Published online: | Jul 2, 2024 |
Identifiers:
| Web of science: | WOS:001315672500042 |
| Scopus: | 2-s2.0-85200413408 |
| OpenAlex: | W4400179176 |
Citing:
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