| Title: | Finite solvable groups with a rational skew-field of noncommutative real rational invariants |
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| Authors: | ID Podlogar, Gregor (Author) |
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| Files: |  PDF - Presentation file, download (2,18 MB)
MD5: FAD9DD00A7DEA6530514A713305F4517
 URL - Source URL, visit https://www.tandfonline.com/doi/full/10.1080/00927872.2022.2156526
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | We consider Noether’s problem on the noncommutative rational functions invariant under a linear action of a finite group. For abelian groups the invariant skew-fields are always rational, for solvable group they are rational if the action is well-behaved – given by a so-called complete representation. We determine the groups that admit such representations and call them totally pseudo-unramified. We show that for a solvable group the invariant skew-field is finitely generated. Finally we study totally pseudo-unramified groups and classify totally pseudo-unramified ▫$p$▫-groups of rank at most ▫$5$▫. |
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| Keywords: | Clifford theory, multiplicity free restrictions, noncommutative Noether’s problem, noncommutative rational invariant, totally unramified groups |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 2268-2292 |
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| Numbering: | Vol. 51, iss. 6 |
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| PID: | 20.500.12556/DiRROS-19164  |
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| UDC: | 512 |
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| ISSN on article: | 0092-7872 |
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| DOI: | 10.1080/00927872.2022.2156526 |
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| COBISS.SI-ID: | 200488195 |
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| Note: |
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| Publication date in DiRROS: | 03.07.2024 |
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| Views: | 759 |
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| Downloads: | 490 |
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