Noether’s Problem for p -Groups with Abelian Normal Subgroups and Central p -Powers

Ivo M. Michailov () and Ivailo A. Dimitrov
Additional contact information
Ivo M. Michailov: Faculty of Mathematics and Informatics, Paisii Hilendarski University of Plovdiv, 24 Tsar Assen Str., 4027 Plovdiv, Bulgaria
Ivailo A. Dimitrov: PMG Nancho Popovich, Str. Kiril I Metodiy 68, 9700 Shumen, Bulgaria

Mathematics, 2024, vol. 13, issue 1, 1-19

Abstract: This paper addresses Noether’s problem for p -groups G , having an abelian normal subgroup of index p , under the condition G p = { g p : g ∈ G } ≤ Z ( G ) —the center of G . We prove that the fixed field K ( G ) = K ( x ( g ) : g ∈ G ) G is rational over K in such cases, focusing on both the classification and structural analysis of these groups. Our results extend existing work by removing restrictive assumptions and providing a refined understanding of p -groups and their representations.

Keywords: Noether’s problem; the rationality problem; nilpotent groups; p-groups; metabelian groups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/1/56/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/1/56/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2024:i:1:p:56-:d:1554713

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().