Year: 2024
Type: article
Abstract: This paper addresses Noether’s problem for p-groups G, having an abelian normal subgroup of index p, under the condition Gp={gp: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.
Source: Mathematics
DOI: 10.3390/math13010056
Authors: Ivo M. Michailov, Ivailo A. Dimitrov
Institution: Plovdiv University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4405849015