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http://hdl.handle.net/11320/19653Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Nelson, Alexander M. | - |
| dc.date.accessioned | 2026-01-26T11:06:33Z | - |
| dc.date.available | 2026-01-26T11:06:33Z | - |
| dc.date.issued | 2025 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 33, Issue 1, Pages 65-83 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/19653 | - |
| dc.description.abstract | We formalize the semidirect product of groups in Mizar, following §10 of Aschbacher’s Finite Group Theory [2]. We also prove the universal property for semidirect products as found in Bourbaki [5, III §2.10] Proposition 7. In an appendix, we define the dihedral group of the regular n-gon and the infinite dihedral group. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | pl |
| dc.subject | semidirect product | pl |
| dc.subject | subgroup complement | pl |
| dc.subject | dihedral group | pl |
| dc.title | Semidirect Products of Groups | pl |
| dc.type | Article | pl |
| dc.rights.holder | 2025 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 4.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2025-0006 | - |
| dc.description.references | Goulnara Arzhantseva and Światosław R. Gal. On approximation properties of semidirect products of groups. Annales Math´ematiques Blaise Pascal, 27(1):1–24, 2020.doi:10.5802/ambp.386 | pl |
| dc.description.references | Michael Aschbacher. Finite Group Theory, volume 10. Cambridge University Press, 2000. | pl |
| dc.description.references | Clia Borlido and Mai Gehrke. Substitution principle and semidirect products. Mathematical Structures in Computer Science, 33(6):486–535, 2023. doi:10.1017/S0960129523000294. | pl |
| dc.description.references | Nicolas Bourbaki. Elements of Mathematics. Algebra I. Chapters 1-3. Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989. | pl |
| dc.description.references | Nicolas Bourbaki. General Topology: Chapters 1–4. Springer Science and Business Media, 2013. | pl |
| dc.description.references | Peteris Daugulis. Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups. Algebra and Discrete Mathematics, 23(2):204–215, 2017. | pl |
| dc.description.references | David S. Dummit and Richard M. Foote. Abstract Algebra. Wiley and Sons, Third edition, 2004. | pl |
| dc.description.references | Wolfgang Gaschutz. Zu einem von B. H. und H. Neumann gestellten Problem. Mathematische Nachrichten, 14(4–6):249–252, 1955. doi:10.1002/mana.19550140406. | pl |
| dc.description.references | Craig R. Guilbault, Brendan Burns Healy, and Brian Pietsch. Group boundaries for semidirect products with Z. Groups, Geometry, and Dynamics, 2024. doi:10.4171/GGD/750. | pl |
| dc.description.references | Scott Harper and Peiran Wu. Classifying the groups of order pq in Lean. arXiv preprint arXiv:2501.09769, 2025. | pl |
| dc.description.references | I. Martin Isaacs. Finite Group Theory, volume 92 of Graduate Studies in Mathematics. American Mathematical Society, 2008. | pl |
| dc.description.references | Vipul Kakkar and Ratan Lal. Automorphisms of semidirect products fixing the nonnormal subgroup. Jordan Journal of Mathematics and Statistics, 17(2):241–248, 2024. doi:10.47013/17.2.5. | pl |
| dc.description.references | Artur Korniłowicz. On the group of inner automorphisms. Formalized Mathematics, 5 (1):43–45, 1996. | pl |
| dc.description.references | Artur Korniłowicz. The product of the families of the groups. Formalized Mathematics, 7(1):127–134, 1998. | pl |
| dc.description.references | Alexander M. Nelson. Internal direct products and the universal property of direct product groups. Formalized Mathematics, 31(1):101–120, 2023. doi:10.2478/forma-2023-0010. | pl |
| dc.description.references | Colin Rothgang, Artur Korniłowicz, and Florian Rabe. A new export of the Mizar Mathematical Library. In Fairouz Kamareddine and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics, pages 205–210, Cham, 2021. Springer International Publishing. doi:10.1007/978-3-030-81097-9 17. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 33 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 65 | pl |
| dc.description.lastpage | 83 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0002-3292-4035 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2025, Volume 33, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Semidirect_Products_of_Groups.pdf | 320,28 kB | Adobe PDF | Otwórz |
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