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On the Group of Computable Automorphisms of the Linear Order of the Reals. / Kornev, Ruslan.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Science and Business Media Deutschland GmbH, 2024. p. 405-419 32 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14773 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Kornev, R 2024, On the Group of Computable Automorphisms of the Linear Order of the Reals. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)., 32, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14773 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 405-419, 20th Conference on Computability in Europe, Amsterdam, Netherlands, 08.07.2024. https://doi.org/10.1007/978-3-031-64309-5_32

APA

Kornev, R. (2024). On the Group of Computable Automorphisms of the Linear Order of the Reals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 405-419). [32] (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14773 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-64309-5_32

Vancouver

Kornev R. On the Group of Computable Automorphisms of the Linear Order of the Reals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Science and Business Media Deutschland GmbH. 2024. p. 405-419. 32. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-64309-5_32

Author

Kornev, Ruslan. / On the Group of Computable Automorphisms of the Linear Order of the Reals. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Science and Business Media Deutschland GmbH, 2024. pp. 405-419 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

BibTeX

@inproceedings{80fb4edafe134bc180fa69f36265b430,
title = "On the Group of Computable Automorphisms of the Linear Order of the Reals",
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.",
author = "Ruslan Kornev",
note = "The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation.; 20th Conference on Computability in Europe, CiE 2024 ; Conference date: 08-07-2024 Through 12-07-2024",
year = "2024",
doi = "10.1007/978-3-031-64309-5_32",
language = "English",
isbn = "9783031643088",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "405--419",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "Germany",

}

RIS

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T1 - On the Group of Computable Automorphisms of the Linear Order of the Reals

AU - Kornev, Ruslan

N1 - Conference code: 20

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85200413408&origin=inward&txGid=7e6e9dcabd81c6cb1d9a1efb14e94ad1

UR - https://www.mendeley.com/catalogue/8d932efb-6da0-3dc2-ab36-8764fe471c86/

U2 - 10.1007/978-3-031-64309-5_32

DO - 10.1007/978-3-031-64309-5_32

M3 - Conference contribution

SN - 9783031643088

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 405

EP - 419

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Science and Business Media Deutschland GmbH

T2 - 20th Conference on Computability in Europe

Y2 - 8 July 2024 through 12 July 2024

ER -

ID: 60500977