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Title:Finite solvable groups with a rational skew-field of noncommutative real rational invariants
Authors:ID Podlogar, Gregor (Author)
Files:.pdf PDF - Presentation file, download (2,18 MB)
MD5: FAD9DD00A7DEA6530514A713305F4517
 
URL URL - Source URL, visit https://www.tandfonline.com/doi/full/10.1080/00927872.2022.2156526
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
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.
Keywords:Clifford theory, multiplicity free restrictions, noncommutative Noether’s problem, noncommutative rational invariant, totally unramified groups
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2023
Year of publishing:2023
Number of pages:str. 2268-2292
Numbering:Vol. 51, iss. 6
PID:20.500.12556/DiRROS-19164 New window
UDC:512
ISSN on article:0092-7872
DOI:10.1080/00927872.2022.2156526 New window
COBISS.SI-ID:200488195 New window
Note:
Publication date in DiRROS:03.07.2024
Views:498
Downloads:293
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PODLOGAR, Gregor, 2023, Finite solvable groups with a rational skew-field of noncommutative real rational invariants. Communications in algebra [online]. 2023. Vol. 51, no. 6, p. 2268–2292. [Accessed 10 April 2025]. DOI 10.1080/00927872.2022.2156526. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=19164
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Record is a part of a journal

Title:Communications in algebra
Shortened title:Commun. Algebra
Publisher:Taylor & Francis
ISSN:0092-7872
COBISS.SI-ID:25249792 New window

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