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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ivo M. Michailov & Ivailo A. Dimitrov, 2024. "Noether’s Problem for p -Groups with Abelian Normal Subgroups and Central p -Powers," Mathematics, MDPI, vol. 13(1), pages 1-19, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:56-:d:1554713
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